US6779752B1 - Projectile guidance with accelerometers and a GPS receiver - Google Patents

Projectile guidance with accelerometers and a GPS receiver Download PDF

Info

Publication number
US6779752B1
US6779752B1 US10/396,639 US39663903A US6779752B1 US 6779752 B1 US6779752 B1 US 6779752B1 US 39663903 A US39663903 A US 39663903A US 6779752 B1 US6779752 B1 US 6779752B1
Authority
US
United States
Prior art keywords
projectile
gps
data
roll
jamming
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
US10/396,639
Inventor
Joseph A. Ratkovic
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Northrop Grumman Guidance and Electronics Co Inc
Northrop Grumman Systems Corp
Original Assignee
Northrop Grumman Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Northrop Grumman Corp filed Critical Northrop Grumman Corp
Priority to US10/396,639 priority Critical patent/US6779752B1/en
Assigned to LITTON SYSTEMS, INC. reassignment LITTON SYSTEMS, INC. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: RATKOVIC, JOSEPH A.
Priority to PCT/US2003/035849 priority patent/WO2004097329A1/en
Priority to EP03783294A priority patent/EP1606571A1/en
Priority to CA002519935A priority patent/CA2519935A1/en
Priority to JP2004571469A priority patent/JP2006514258A/en
Priority to AU2003290711A priority patent/AU2003290711A1/en
Publication of US6779752B1 publication Critical patent/US6779752B1/en
Application granted granted Critical
Assigned to NORTHROP GRUMMAN SYSTEMS CORPORATION reassignment NORTHROP GRUMMAN SYSTEMS CORPORATION ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: NORTHROP GRUMMAN CORPORATION
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

Links

Images

Classifications

    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41WEAPONS
    • F41GWEAPON SIGHTS; AIMING
    • F41G7/00Direction control systems for self-propelled missiles
    • F41G7/34Direction control systems for self-propelled missiles based on predetermined target position data
    • F41G7/36Direction control systems for self-propelled missiles based on predetermined target position data using inertial references
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41WEAPONS
    • F41GWEAPON SIGHTS; AIMING
    • F41G7/00Direction control systems for self-propelled missiles
    • F41G7/34Direction control systems for self-propelled missiles based on predetermined target position data
    • F41G7/346Direction control systems for self-propelled missiles based on predetermined target position data using global navigation satellite systems, e.g. GPS, GALILEO, GLONASS
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/14Receivers specially adapted for specific applications
    • G01S19/18Military applications
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/21Interference related issues ; Issues related to cross-correlation, spoofing or other methods of denial of service
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/35Constructional details or hardware or software details of the signal processing chain
    • G01S19/36Constructional details or hardware or software details of the signal processing chain relating to the receiver frond end
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42Determining position
    • G01S19/48Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
    • G01S19/49Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/53Determining attitude
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/01Determining conditions which influence positioning, e.g. radio environment, state of motion or energy consumption
    • G01S5/011Identifying the radio environment

Definitions

  • This invention relates to the field of aircraft or projectile attitude determination and estimation using a GPS signal; the system using a first and second linear accelerometer for an estimation of the projectile's roll angle, and information from an additional third accelerometer for a pitch angle estimation; the system further including means for detecting and avoiding the effects of GPS signal jamming.
  • the general problem to be solved is how to guide a gun-fired projectile onto a target with a known geographic location at lowest cost with reasonable reliability.
  • This application addresses a portion of that problem by providing an estimate of the trajectory of the projectile from launch, the initial conditions of the projectile immediately after launch and the distance, direction and altitude to the idealized trajectory calculated for the projectile at the time of launch or firing and by reliably detecting and avoiding the effects of GPS signal jamming.
  • a first approach to the problem to be solved used only a GPS receiver and a turns counter. Although such a system represents a relatively inexpensive solution, it may be vulnerable to GPS jamming. Accordingly, additional measures may need to be implemented to ensure reliable reception and processing of an uncorrupted GPS signal, e.g., protection of the GPS signal.
  • a second approach used a GPS receiver, a turns counter, and a triax of gyros, which adds to the cost of the approach.
  • this second approach requires protection of the GPS signal almost all the way into the target.
  • such protection is required because, in the event the GPS signal is lost, no mechanism exists to account for any external forces that may act on the projectile throughout its flight. Accordingly, a need exists for a system and process for guiding a projectile to a target while minimizing or eliminating the vulnerability of the system and process to interference with, e.g., jamming of, the GPS signal.
  • Prior attempts to meet this need have focused on either preventing interference with the GPS signal or enabling operation with limited GPS data. Attempts to enable operation with limited GPS data have typically involved increasing the performance and/or functionality of the inertial instruments on board the projectile. For example, to address the inability of the above-mentioned second approach to account for the projectile's reaction to external forces if/when the GPS signal may be lost, additional accelerometers may be incorporated into the system to enable compensation for the projectile's reaction to external forces, i.e., the sensor package may comprise a complete IMU.
  • ZLG zero lock gyros
  • gyroscopic instruments are typically subject to failure modes and uncertainties relating to launch accelerations in the range of 15,000-30,000 Gs.
  • use of these technologies usually requires that the vehicle carry at least one gyro in a gimbaled or strap-down arrangement with the attendant disadvantages of cost, weight and power dissipation.
  • a projectile without gyros is guided toward a target using a GPS signal and a triax of accelerometers.
  • a computer-implemented process uses GPS position and GPS delta velocity data along with data from-the accelerometer triax to determine the projectile's estimated attitude in pitch, roll and yaw.
  • the computer-implemented process determines the projectile's attitude in navigational coordinates and creates a time indexed record of the projectile's trajectory after the on-board GPS receiver locks on to the required number of satellites.
  • the data in the time indexed record of the trajectory is filtered and smoothed.
  • the accelerometers are used to measure the forces acting on the projectile and the projectile's rotation rates.
  • the GPS is used to provide data for the calculation of initial aiming and velocity errors and for the calibration of the accelerometers when positioned in the gun barrel prior to launch.
  • an aspect of the present invention provides for improved reliability of GPS signals.
  • GPS signal data may be acquired from GPS signals transmitted from one or more satellites and received by one or more antennas on the projectile.
  • one or more corresponding GPS signal jamming detector may be included to monitor each GPS signal and to detect whether each GPS signal has been subjected to jamming. If such jamming is detected, an anti-jammer will implement GPS signal protection measures.
  • Exemplary GPS signal protection measures may include causing the projectile to engage, or remain engaged, in a periodic motion, e.g., rolling, and using the periodic motion of the projectile to selectively sample GPS signals in such a manner as to detect and omit jammed GPS signals and to enable reliable processing of unjammed signals, e.g., by selectively and periodically avoid GPS signals that exhibit jamming. It should be noted that as a projectile proceeds through each cycle of its periodic motion, i.e., each rolling revolution, each of the one or more antennas will periodically be positioned to receive a GPS signal from each of the one or more satellites.
  • each of the one or more antennas will periodically be free from jamming, e.g., during at least a portion of the roll attitude.
  • exemplary GPS signal protection measures may include detecting whether a GPS signal received by one or more of the antennas is free from jamming and switching a GPS receiver to use only the unjammed signals. It should be noted that in such an exemplary embodiment, the projectile need not be spinning or rolling. Accordingly, this protection measure may be implemented with projectiles that are not roll-stabilized. It should also be noted that, in accordance with this embodiment, the antenna(s) may be decoupled from the main body of the projectile via a mechanism such as a slip ring.
  • the projectile may be spinning or roll stabilized while the antennas are maintained in a fixed orientation with respect to one or more satellites.
  • the projectile may be stationary while the antennas undergo periodic motion, e.g., spinning, with respect to one or more satellites.
  • exemplary protection measures may include conversion of the GPS signal from an RF signal to a digital signal as well as implementation of an automatic gain control.
  • each GPS signal may be converted by a high speed analog to digital converter immediately, or very soon, after it is received.
  • the converted digital GPS signal may be passed through a digitally implemented automatic gain control circuit. Both the analog to digital converter and the automatic gain control circuit may be implemented in the GPS radio receiver.
  • FIG. 1 is a perspective and exploded view of a projectile or unmanned airborne device equipped with an on-board GPS receiver, a set of accelerometers coupled to a vehicle frame, a plurality of antennas, and on-board computer cards for executing the invention process;
  • FIG. 2 shows a launch vehicle and a desired trajectory with a flight error envelope region around the trajectory
  • FIGS. 3 a , 3 b , 3 c and 3 d each show a block diagram for processing accelerometer and GPS data for the purpose of estimating the trajectory of flight;
  • FIG. 4 is a perspective schematic view of an aircraft showing a typical coordinate system and defining angles of rotation;
  • FIG. 5 is a block diagram for the functional steps in a Roll Angle Computation
  • FIG. 6 is a flow chart for the steps in a typical Kalman filter and for calculating an alternate roll angle
  • FIG. 7 a is a flow chart of the forward filter steps in a typical smoother
  • FIG. 7 b is a flow chart of the backward filter steps in a typical smoother.
  • FIG. 8 illustrates time dependent GPS signals as received by a plurality of antennas on a rotating projectile in the presence of GPS signal jamming.
  • FIG. 1 schematically shows the major components in an exemplary embodiment of a projectile guidance system without gyros 10 distributed in the exploded perspective view of a projectile 12 .
  • the projectile 12 is depicted in flight after having been fired from a gun (not shown).
  • the projectile is shown having an orthogonal body fixed coordinate system.
  • the rotation rate components in roll ⁇ with a longitudinal axis X b , a pitch axis Y b and a yaw axis z b .
  • FIG. 4 shows an aircraft with a corresponding orthogonal body coordinate system.
  • the rotation rate components in roll ⁇ , pitch ⁇ and yaw ⁇ are defined in FIG. 4.
  • a locally level fixed earth navigational coordinate system is also depicted in FIG. 4 .
  • the Y N axis is typically parallel to a meridian of longitude and points true north.
  • the X N axis is parallel to a parallel of latitude and points east and the Z N axis extends from the surface of the earth as a gravity vector.
  • the angle a is used in a navigation system to traverse the poles of the earth without encountering position singularities.
  • components of time indexed data elements such as projectile acceleration and velocity are transformed from the body coordinates, indicated by a subscript “b” into the earth referenced coordinate data elements indicated by a subscript N using conventional direction cosine matrices.
  • the projectile guided by the projectile guidance system without gyros, has a triax of accelerometers 14 .
  • the triax has an x-axis accelerometer for providing x-axis acceleration data measured along the x b axis, a y-axis-accelerometer for providing y-axis acceleration data measured along the Y b axis and a z-axis accelerometer for providing z-axis acceleration data measured along the z b axis.
  • a GPS antenna represented by band 16 and a GPS receiver represented by module 18 represent a means for providing onboard GPS position and altitude and GPS velocity data in earth referenced navigational coordinates.
  • Alternative antenna patterns 88 , 89 are configured to receive GPS data from one or more satellite 78 , 79 . While only antenna patterns 88 , 89 and antenna band 16 are shown, it should be noted that any number, configuration, and/or orientation of antennas may be included on the projectile, each antenna being configured and oriented to receive GPS signals from a different direction or range of directions (e.g., each antenna pattern having a lobe directed toward a different direction or range of directions). Similarly, although only one GPS receiver 18 is shown, it should be noted that a plurality of GPS receivers may be implemented to accommodate processing of the GPS signals received through the specific number, configuration and orientation of antennas implemented on the projectile.
  • Module 20 represents a guidance processor which provides the function of a computer, memory and program means for storing and accessing time indexed GPS position and GPS velocity data, for implementing GPS signal protection measures as described herein, and for transforming the x, y and z axis acceleration data from body to navigation coordinates.
  • the acceleration data is arrayed and has time indexes that are common with the time indexes for the GPS position and velocity data.
  • a turns counter 22 provides an ac signal in flight representing the angular rate of rotation of the projectile in the earth's magnetic field.
  • the computer, memory and program means on module 20 receives and responds to corresponding time indexed acceleration data, GPS velocity and position data for calculating and outputing corresponding sets of time indexed estimates of the projectile roll, pitch and yaw angles with respect to the locally level earth referenced navigation coordinates for each time index iteration of the program to provide present position, velocity and acceleration data to a flight control and ballistic data system represented by module 26 for it to use in guiding the projectile to a predetermined target location.
  • the flight control and ballistic data system controls the projectile by providing commands to control surfaces such as canards 28 , 30 to keep the projectile on a trajectory to the target location.
  • control surfaces such as canards 28 , 30 to keep the projectile on a trajectory to the target location.
  • the selection and or design of a flight control and ballistic data system represented by card or module 26 is believed to be a design choice and is not the subject of this invention disclosure. Nevertheless, if the projectile is engaged in periodic motion, e.g., rolling, the present invention provides that trajectory corrections may be made by waiting for an orientation of a control surface to correspond with a direction in which it is desirable to steer the projectile.
  • the present invention also contemplates that if the trajectory corrections are large and the projectile guidance section is roll stabilized, then the projectile can be de-spun and the corrections made while the projectile is in a roll-stabilized mode. Then, after completing the corrections, the projectile can go back to being a rolling airframe.
  • the present invention enables these capabilities by providing a mechanism for determining the roll orientation of the projectile.
  • the roll orientation of the projectile may be determined through: 1) a roll gyro, 2) the roll position of GPS satellites as they turn on/off, 3) GPS attitude determination with multi antennas, and 4) a magnetic turns counter.
  • GPS signal data may acquired from GPS signals transmitted from one or more satellites 78 , 79 and received by one or more antennas 88 , 89 on the projectile.
  • a plurality of GPS antenna patterns 88 , 89 receive GPS signals which are passed through RF processing means 98 , 99 to produce RF processed GPS signal 3344 .
  • Information from a high speed correlator 3354 , and roll reference 3364 are transmitted to processor 3375 along with RF processed GPS signal 3344 .
  • processor 3374 Based on signals 3344 , 3354 , and 3364 , processor 3374 produces a position signal 3381 , a velocity signal 3382 , and an attitude signal 3383 .
  • each GPS signal 3407 may be sent through a low noise amplifier 3417 before being received by radio 3427 .
  • one or more GPS signal jamming detectors 3418 may be included to monitor each GPS signal 3407 and to detect whether each GPS signal has been subjected to jamming. If such jamming is detected, an anti-jammer 3419 may implement GPS signal protection measures which may, for example, selectively and periodically avoid GPS signals that exhibit jamming based on the periodic motion of the antenna portion of the projectile.
  • jamming detector 3418 and anti-jammer 3419 transmit signals to system processor 3457 , which also receives information from roll reference 3467 and GPS receiver 3437 .
  • digital filters 3427 Based on signals received from system processor 3457 , digital filters 3427 receive GPS signals from radio 3427 and selectively transmit unjammed portions of those GPS signals to GPS receiver 3437 . GPS receiver 3437 then uses pre-stored data 3447 to process and transmit GPS signals to system processor 3457 . Finally, system processor 3457 utilizes roll reference 3467 and GPS signal to transmit signals to autopilot 3477 , which causes control surfaces 3487 to be actuated, thereby guiding the projectile to a target.
  • a GPS signal protection measure involves causing the projectile to engage, or remain engaged, in a periodic motion (e.g., spinning, rolling, or otherwise oscillating) and using the periodic motion of the projectile to selectively sample GPS signals in such a manner as to detect and omit jammed GPS signals and to enable reliable processing of unjammed signals.
  • a periodic motion e.g., spinning, rolling, or otherwise oscillating
  • each of the one or more antennas 88 , 89 will periodically be positioned to receive a GPS signal from each of the one or more satellites 78 , 79 .
  • each of the one or more antennas will periodically be free from jamming, e.g., during at least a portion of the roll attitude.
  • FIG. 8 illustrates three exemplary time-dependent GPS signals as received by three corresponding GPS antenna and receiver means implemented on a projectile undergoing periodic motion, e.g., spinning.
  • a first GPS signal exhibits jamming as the projectile rotates through an orientation from approximately 30 degrees to an orientation of approximately 210 degrees.
  • a second GPS signal exhibits jamming as the projectile rotates through an orientation from approximately 120 degrees to an orientation of approximately 360 degrees.
  • a third GPS signal exhibits jamming as the projectile rotates through an orientation from approximately 360 degrees to an orientation of approximately 30 degrees.
  • an substantially continuous unjammed GPS signal may be received by switching on the first antenna as the projectile rotates between approximately 210 degrees and approximately 30 degrees, by switching on the second antenna as the projectile rotates between approximately 360 degrees and approximately 120 degrees, by switching on the third antenna as the projectile rotates between approximately 30 degrees and approximately 360 degrees, by switching off the first antenna as the projectile rotates between approximately 30 degrees and approximately 210 degrees, by switching off the second antenna as the projectile rotates between approximately 120 degrees and approximately 360 degrees, and by switching off the third antenna as the projectile rotates between approximately 360 degrees and approximately 30 degrees.
  • the flight control and ballistic data system 26 is pre-programmed to use information provided via bus 32 from the projectile guidance system without gyros 12 , after launch, to de-spin the projectile and to roughly position the top of the projectile skyward, or to otherwise orient an antenna pattern 88 , 89 , so as to optimize the reception of GPS signals.
  • the accelerometers are un-caged and activated.
  • the computer, memory and program means then performs its first estimate and update of the state matrix including an estimate of the vehicle rates.
  • the anti-jammer 3419 may detect that a GPS signal 3407 received by one or more of the antennas is free from jamming and may switch or otherwise cause the one or more GPS receiver 18 to use only the unjammed signal. It should be noted that in such an exemplary embodiment, an unjammed GPS signal may be received without requiring the projectile to be rolled. To accomplish this, a computer-implemented process may be implemented as a guidance program configured to cause the projectile to maintain an orientation of the GPS antenna and receiver means so as to permit one or more antenna to substantially continuously receive an unjammed GPS signal.
  • the projectile need not be spinning or rolling. Accordingly, this protection measure may be implemented with projectiles that are not roll-stabilized.
  • the antenna(s) may be decoupled from the main body of the projectile via a mechanism such as a slip ring. Accordingly, the projectile may be spinning or roll stabilized while the antennas are maintained in a fixed orientation with respect to one or more satellites. Similarly, the projectile may be stationary while the antennas undergo periodic motion, e.g., spinning, with respect to one or more satellites.
  • the projectile may either be spinning or roll stabilized, e.g., by decoupling it from the main body of the projectile via a slip ring.
  • the anti-jamming means may be configured to cause the projectile to engage in a periodic motion and to selectively and periodically avoid GPS signals that exhibit jamming.
  • exemplary protection measures may include immediate conversion of the GPS signal from an RF signal to a digital signal as well as implementation of an automatic gain control.
  • each GPS signal may be converted immediately or very soon after it is received by a high speed analog to digital converter. Then, the digital GPS signal may pass through a digitally implemented automatic gain control circuit. Both the analog to digital converter and the automatic gain control circuit may be implemented in the GPS radio receiver.
  • the system may be configured to be initialized prior to firing.
  • the system may determine and store in memory which satellites will be in the field-of-view (FOV) of each antenna pattern 88 , 89 throughout the trajectory of the projectile and which combination of satellites 78 , 79 gives the best GDOP for the trajectory. This information is pre-stored in the receiver 18 along with any other correction data that may be available.
  • FOV field-of-view
  • the GPS signals 3407 are transmitted through a low noise amplifier 3417 to a radio receiver 3427 , which may comprise a high speed analog to digital converter (e.g., a 5 gigabit/second analog to digital converter with 14 bits of resolution).
  • Radio receiver 3427 may also comprise a digitally implemented automatic gain control circuit.
  • the signals are then sent to a set of digital filters 3427 as well as one or more jamming detector 3418 .
  • a separate filter 3427 may be implemented for each pre-selected satellite 78 , 79 that will be used in the TOA computation.
  • digital filters 3427 may be dynamically tuned in real time to band pass the frequency of each pre-selected satellite.
  • the center of the band pass will be the GPS carrier frequency adjusted for Doppler motion between the projectile and the satellite.
  • the GPS signals are then sent to the GPS receiver 3437 where they are correlated against the known code of each of the pre-selected satellites via a high speed digital correlator 3447 , and position and velocity determined.
  • rate information is extracted by separating the accelerometer ac signal from the dc or steady state signal. As the projectile rolls, the pitch and yaw accelerometers output signals will vary as a sine wave function. If the vehicle is not rolling, then data is extracted and transferred from the body coordinate system to the earth referenced navigation coordinate system using DCM (direction cosine matrix) relationships as required.
  • DCM direction cosine matrix
  • FIG. 2 shows a mobile artillery weapon, firing a projectile toward a target.
  • ⁇ right arrow over (X) ⁇ (t) True is a vector quantity representing the computed true position of the projectile as a function of time.
  • ⁇ right arrow over (X) ⁇ (t) Nominal is a vector representing the ideal location of the projectile on the ideal trajectory.
  • ⁇ right arrow over (X) ⁇ ( 0 ) Error is a vector representing the position error of the projectile at time zero before launch.
  • ⁇ right arrow over (X) ⁇ (t) Error is a vector representing the error in the projectiles position due to accumulated errors resulting from navigational instrument error and GPS errors.
  • the figure shows the sequence of events and schematically portrays an error budget region in dashed lines that concludes with an ellipse representing the TARGET ERROR that can result from launching the projectile using conventional artillery practice with no on board guidance.
  • the funnel region in a continuous line schematically shows the position error of an on-board GPS progressively diminishing and asymptotically approaching a limit that is much smaller than the TARGET ERROR limit for a trajectory with no on board guidance.
  • the invention projectile guidance system without gyros 10 uses a triad of accelerometers to provide real time body referenced data to a computer, memory and program means and real time position data from a GPS to establish and output the attitude of the projectile.
  • the outputs are Kalman filtered and coupled to the flight control and ballistic data system represented by module 26 shown in FIG. 1 along with the aiding GPS position data for use in steering the projectile into the region bounded by the funnel region.
  • FIGS. 3 a and 3 b schematically show an embodiment of a data flow used by the projectile guidance system without gyros 10 .
  • Phantom block 300 represents the function provided by a fire control and ballistics computer as it executes an initialization program to process data received from data sources such as an external input of a TARGET LOCATION, the geographic location of the weapon launching the projectile, the PROJECTILE TYPE, the PITCH ALIGNMENT IN BARREL, the pitch angle of the launching tube, the outputs of the triax 304 of three components of acceleration a x , a y and a z , in body coordinates, the roll angle ROLL ⁇ , and the roll rate ROLL RATE ⁇ from the spin counter 308 .
  • data sources such as an external input of a TARGET LOCATION, the geographic location of the weapon launching the projectile, the PROJECTILE TYPE, the PITCH ALIGNMENT IN BARREL, the pitch angle of the launching tube, the output
  • the FIRE CONTROL AND BALLISTICS computer processes the data available and prior to launch transfers the initial state data such the initial orientation angles, body fixed angle rates, present position and initial velocity components.
  • the spin counter 308 and the triax 304 provide their outputs directly to the INITIAL PROJECTILE STATE ESTIMATE 312 via signal paths 314 and 333 respectively. It is most likely that all initial conditions would be input into the projectile from an external source such as the FIRE CONTROL AND BALLISTICS function 302 via an electrical, magnetic or optical link, or perhaps mechanical link.
  • the initial conditions would have to be extended to include data such as the ship's velocity, heading, displacement from the ship's inertial guidance computer, and possibly the coordinates of the gun with respect to the station from which the gun is receiving its initial condition information.
  • the FIRE CONTROL AND BALLISTICS function 302 also provides roll indexing information to the spin counter 308 to provide a zero reference.
  • the spin counter 308 provides estimates of roll angle ⁇ b to an accuracy of a few degrees, as well as roll rate ⁇ b the FIRE CONTROL AND BALLISTICS function 302 precomputes an expected ballistic trajectory which is also passed to the projectile.
  • This ballistic information, along with accelerometer information, or data directly from the FIRE CONTROL AND BALLISTICS function 302 is used to determine the initial state vector and attitudes of the projectile at initialization of the estimation process.
  • the algorithm is initialized when both the accelerometer and the GPS data are available for state estimation.
  • the FIRE CONTROL AND BALLISTICS function 302 also receives a set of initial states for orientation and position of the projectile via signal path 320 from the ESTIMATION OF NEW INITIAL TARGET STATE function 322 as a result of a failure of a fit test.
  • the FIRE CONTROL AND BALLISTICS function 302 outputs a set of initial STATE ESTIMATES to the INITIAL PROJECTILE STATE ESTIMATE functional block 312 which transfers initial BODY STATE ESTIMATES ⁇ right arrow over (V) ⁇ 0 , ⁇ right arrow over (x) ⁇ 0 via signal path 324 to SMOOTHING PROCESS function block 344 and a set of ATTITUDE STATE ESTIMATES via signal path 330 to the initial state estimate of the initial attitude angle array in ATTITUDE FILE 332 .
  • the turns or SPIN COUNTER 308 which provided turn count data to the FIRE CONTROL AND BALLISTICS function 302 also provides turn count data via signal line 333 to the INITIAL PROJECTILE STATE ESTIMATE FUNCTION block 312 and to the time indexed SPIN COUNTER MEASURED DATA memory array represented on FIG. 3 b by functional block 350 where the total roll angle ⁇ (n) of the projectile is accumulated and time indexed and transferred via path 351 to the ATTITUDE ESTIMATION ALGORITHM 372 .
  • Spin counter technology is a mature technology. The Alliant Techsystems company has reportedly developed one small enough to fit into a 20 mm projectile. A turns counter for larger diameter projectiles is therefore a product that can be purchased for use in the invention system and process without difficulty.
  • the output of the turns counter is a sine wave output as the projectile rotates through the Earth's Magnetic Field.
  • the INITIAL PROJECTILE STATE ESTIMATE FUNCTION block 312 provides initial ATTITUDE STATE ESTIMATE values for azimuth ⁇ 0 , pitch ⁇ 0 and roll ⁇ 0 angle to the ATTITUDE FILE 332 in FIG. 3 b as initial values.
  • the outputs of the triax 304 of three components of acceleration a x a y and a z in body coordinates are processed by the function represented by the block 336 to transfer time indexed body referenced changes in velocity via signal path 338 to the ACCEL DATA FILE memory array 340 .
  • the ACCEL DATA FILE memory array 340 couples an array of time indexed acceleration data elements to the SMOOTHING PROCESS function block 344 .
  • the filtering and smoothing process of block 344 will be discussed in connection with FIGS. 6, 7 a and 7 b later in this disclosure.
  • the smoothing process uses the initial estimates of attitude, velocity and position in conjunction with the present accelerometer data to determine velocity and position of the projectile in body coordinates.
  • the output of the smoothing process are STATE VECTOR ESTIMATES, ⁇ right arrow over (X) ⁇ B(n) , ⁇ right arrow over (V) ⁇ B(n) for position and velocity which are coupled via signal path 346 to the BODY TO INERTIAL TRANSFORMATION functional block 348 .
  • the GPS MEASURED DATA function block 356 periodically receives time indexed velocity and position data ⁇ right arrow over (V) ⁇ (n) and ⁇ right arrow over (X) ⁇ (n) and transfers the data via signal path 358 into the time indexed array in the computer, memory and program means memory shown as function block 360 .
  • the GPS velocity and position data is transferred via signal path 362 to a Kalman filter represented by function block 364 .
  • the Kalman filter transfers filtered values of the projectile's estimated present position and velocity vectors via signal path 368 to the FIT ERROR TEST functional block 370 and to the ATTITUDE ESTIMATION ALGORITHM functional block 372 .
  • the ATTITUDE FILE 332 transfers time indexed estimated attitude angles and attitude angular rate data to the ATTITUDE ESTIMATION ALGORITHM functional block 372 via signal path 374 and to the BALLISTICS ESTIMATE (n) functional block 376 via transfer path 378 in earth referenced navigational coordinates.
  • the BALLISTIC ESTIMATES uses the known model characteristics of the projectile with the corrected initial position and initial velocity information via path 375 and the history of all past attitude and attitude rates from path 378 to provide a modeled estimate of the present position and velocity via path 382 to the ATTITUDE ESTIMATION ALGORITHM 372 .
  • the filtered body STATE VECTOR ESTIMATES ⁇ right arrow over ( ⁇ circumflex over (X) ⁇ ) ⁇ B(n) , ⁇ right arrow over ( ⁇ circumflex over (V) ⁇ ) ⁇ B(n) vectors in the orthogonal body coordinate system, are transferred via signal path 346 to the BODY TO INERTIAL TRANSFORMATION block 348 .
  • the BODY TO INERTIAL TRANSFORMATION block 348 receives the estimated attitude angles and attitude angular via signal paths 384 and 386 and processes the STATE VECTOR ESTIMATES from representation in the orthogonal body coordinate system into vectors in the earth referenced navigational coordinate system to position and velocity estimates in earth referenced navigational coordinates using conventional direction cosine transformations such as those explained in the text by George Siouris, titled “Aerospace Avionics Systems, A Modern Synthesis”, published by Academic Press, published in 1993.
  • This estimation process can be simplified and improved using measured turns counter data and by computing a new ballistic trajectory based on new initial state information.
  • the BODY TO INERTIAL TRANSFORMATION functional block 348 outputs the estimated position and velocity STATE VECTOR ESTIMATES in earth referenced navigational coordinates via signal path 388 to the FIT ERROR TEST functional block 370 where the STATE VECTOR ESTIMATES are compared to the Kalman filtered GPS position and velocity. It is not possible in a statistical sense to make the estimation process fit better than the GPS position and the errors associated with the GPS. If the error for the differences between the two state vectors is less than 1 or 2 times the GPS error, the algorithm declares the fit to be “statistically good enough” to quit and wait for a new measured data point to arrive. If the test passes, the estimates of position, velocity, attitude and attitude rates are used to update the n ⁇ 1 position in the estimated position and attitude time indexed memory arrays.
  • the algorithm estimates a new set of initial projectile states via a perturbation algorithm and repeats the estimation process again, until the solution converges to limits within the predetermined fit error criteria. If the test fails, a FAIL signal is coupled via path 390 to the ESTIMATION OF NEW INITIAL TARTET STATE functional block 322 which adjusts the initial position, velocity, attitude and attitude rates and couples a modified set of estimated state data via signal path 320 into the INITIAL PROJECTILE STATE ESTIMATE functional block 312 for an additional cycle. Iteration continues until the initial conditions are adjusted to obtain a PASS signal out of functional block 370 followed by the next data iteration using GPS data one second later.
  • inertial instruments e.g., inertial instruments performing at levels better than 100 micro g
  • Honeywell's VBA accelerometers and Silicon Accelerometer supplied from the Litton Guidance & Control Systems Div. of Northrop Grumman Inc. at Woodland Hills, Calif. 91637, the assignee, have such a capability.
  • a GPS Receiver by Alliant Techsystems is available for use in the invention system and process.
  • the Alliant GPS uses a type 509 processor that has sufficient processing power and a separate memory which can be used to store user software and the system processor for this application.
  • the Alliant receiver is configured with multiple RF front ends to accommodate multiple antenna inputs as a means of protecting the GPS signal as the projectile rolls.
  • the GPS 509 processor can also be used to process the data and integrate the inertial data with the GPS and turns counter data.
  • Software can be incorporated into the 509 processor to extract rate information from the accelerometer triax and integrate the data from the sensors.
  • GPS signal data may acquired from GPS signals transmitted from one or more satellites 78 , 79 and received by one or more antennas 88 , 89 on the projectile.
  • GPS signal jamming detector 3418 may be included to monitor each GPS signal 3407 and to detect whether each GPS signal 3407 has been subjected to jamming. If such jamming is detected, an anti-jammer 3419 may implement GPS signal protection measures present in system processor 3457 .
  • anti-jammer 3419 may cause system processor 3457 to cause the projectile to engage, or remain engaged, in a periodic motion such as rolling or spinning.
  • a periodic motion such as rolling or spinning.
  • each of the one or more antennas 88 , 89 may periodically be positioned to receive a GPS signal from each of the one or more satellites 78 , 79 .
  • at least one GPS signal from a satellite remains capable of being by one or more antenna in an unjammed state, each of the one or more antennas will periodically be free from jamming, e.g., during at least a portion of the roll attitude.
  • anti-jammer 3419 may cause system processor 3457 to de-spin the projectile and to roughly position the top of the projectile skyward, or to otherwise orient an antenna pattern 88 , 89 , so as to optimize the reception of GPS signals 3407 .
  • the accelerometers are un-caged and activated.
  • the computer, memory and program means then performs its first estimate and update of the state matrix including an estimate of the vehicle rates.
  • the anti-jammer 3419 may switch or otherwise cause the one or more GPS receiver 18 or the system processor 3457 to use only the unjammed GPS signal received by the one or more of the antennas that is free from jamming.
  • the roll angle of a guided projectile is typically provided by a gyro or a gyro platform.
  • a roll angle signal characterizing the roll angle of the projectile is necessary to enable a flight control system to drive the flight control surfaces, such as canards, to roll the projectile to the left or right as required, to use lift from its lift surfaces to change the heading of the projectile to one directed to a target. It is an objective of this disclosure to provide a mathematical and therefore, a computer programmable process, for generating the roll angle of the projectile without signals from a gyro and by using the accelerometer outputs of a triax and the position and velocity signals from a GPS.
  • ⁇ right arrow over (x) ⁇ denotes a vector with no specific reference frame of resolution.
  • ⁇ right arrow over (x) ⁇ b denotes a vector resolved in a coordinate frame called the body-frame or projectile-frame.
  • All coordinate frames discussed herein, including the body-frame coordinates, are right-handed orthogonal frames that have x, y, and z axes that extend from a location in the body of the projectile, such as the center of gravity, or origin designated as a reference point “O” to form an orthogonal triad extending in the forward or positive “X b ” axis direction, in the right or positive “y b ” axis direction and down in the positive “Z b ” axis directions.
  • At least two accelerometers are fixed to and aligned with the body-frame along the y and z b axes.
  • the principal axes of the b-frame coincide with the input axes of the inertial sensors and intersect at the origin “O”.
  • a second coordinate frame of interest is the geographic or earth referenced navigational coordinate system or frame with principal axes X, Y and Z that coincide with the East, North, and Up directions as shown at the bottom of FIG. 4 .
  • Time dependency of a quantity is indicated with round brackets around a time variable or index.
  • C N b (t 1 ) denotes the value of the DCM for the conversion from navigational to body-frame coordinates at time t 1 .
  • the transpose of the C N b (t 1 ) DCM provides C b N (t 1 ), the DCM for the conversion from body-frame to navigational-frame coordinates at time t 1 .
  • An increment of a variable is indicated with the symbol ⁇ .
  • ⁇ right arrow over (x) ⁇ denotes the increment of the vector ⁇ right arrow over (x) ⁇ over a predefined time interval.
  • An error in a variable is indicated with the symbol ô.
  • ô ⁇ right arrow over (x) ⁇ denotes the error in the vector ⁇ right arrow over (x) ⁇ .
  • the symbol indicates an approximate or substantially close equality.
  • a first accelerometer is positioned to sense acceleration along the y b body axis that extends outward from the right side of the body.
  • a second accelerometer is positioned to sense acceleration along the z b body axis that extends downward from the origin forming the yaw axis.
  • a third accelerometer is positioned to sense acceleration along the x b or forward axis.
  • the accelerometer outputs are resolved from-body coordinates into navigational coordinate values in accordance with the following equation:
  • a N C N b
  • a B ⁇ T ⁇ H ⁇ T ⁇ P ⁇ T ⁇ R ⁇ T A B 1a.
  • a b represents the acceleration vector in body coordinates
  • the bracketed H, P and R operators ⁇ H ⁇ T , ⁇ P ⁇ T ⁇ R ⁇ T individually represent the transpose of the positive rotation DCM transformation steps from body to navigational coordinates for the heading or yaw, about zb, pitch, about y and roll, about xb, of the vehicle or projectile fixed coordinate system, in that sequence, to obtain the acceleration vector A N as elements of vehicle acceleration in navigation coordinates with components along the fixed navigation or earth referenced East, X, North, Y and Up, Z axis.
  • the data elements of acceleration A b from the triad of accelerometers on the projectile, are integrated over a predetermined incremental time interval such as one second to obtain incremental changes in velocity in navigational coordinates in accordance with the following equation:
  • GPS data Concurrent with each calculation of the incremental change in velocity based on accelerometer data, GPS data is used to calculate an incremental change in velocity.
  • the GPS data is already in navigational coordinates. The following equation is used:
  • a double integration is performed on the body accelerometer data along with a body to navigation frame transformation to obtain the change in position based on transformed. accelerometer data from the body frame using the following equation:
  • the pitch angle is the angle of the barrel at firing and the beading is the angle ⁇ that the barrel makes with true north at firing. Both are available from initialization from the system and are expected to be close to the normal trajectory with time, and therefore nominally known.
  • ⁇ R ⁇ A B ⁇ Q ⁇ ( ⁇ V GPS ) 13a.
  • ⁇ R ⁇ A B ⁇ Q ⁇ ( ⁇ P GPS ) 13b.
  • ⁇ circumflex over (x) ⁇ b , ⁇ b and ⁇ circumflex over (z) ⁇ b are unit vectors along the body axis.
  • the incremental accelerometer and velocity data from the GPS is made available in fixed navigation coordinates forming two three-element vectors
  • ⁇ overscore ( ⁇ V GPS ) ⁇ ⁇ V x ⁇ circumflex over (x) ⁇ + ⁇ V y ⁇ + ⁇ V z ⁇ circumflex over (z) ⁇ and 16a.
  • ⁇ overscore ( ⁇ V GPS ) ⁇ ⁇ P x ⁇ circumflex over (x) ⁇ + ⁇ V y ⁇ + ⁇ V z ⁇ circumflex over (z) ⁇ a 16b.
  • ⁇ circumflex over (x) ⁇ , ⁇ and ⁇ circumflex over (z) ⁇ are basic unit vectors of the East, North and Up coordinate frame system.
  • a 1 [ a 2 ⁇ a 3 a 3 - a 2 a 2 ⁇ a 3 a 3 - a 2 ] 20 ⁇ d .
  • ⁇ 1 [ q 21 q 22 q 23 0 0 0 q 31 q 32 q 33 0 0 0 0 0 0 q 21 q 22 q 23 0 0 0 q 31 q 32 q 33 ] 20 ⁇ e .
  • w 1 _ [ ⁇ ⁇ ⁇ V X ⁇ ⁇ ⁇ V Y ⁇ ⁇ ⁇ V Z ⁇ ⁇ ⁇ V X ⁇ ⁇ ⁇ V Y ⁇ ⁇ ⁇ V Z ] 20 ⁇ f .
  • Equation 20c is the unknown roll quantity. Rewriting Equation 20c provides:
  • Equation 21 for ⁇ overscore ( ⁇ ) ⁇ 1 , recognizing that Equation 21 represents four equations in two unknowns (CR, SR), proceeds with multiplying both sides of Equation 21 by a′ 1 a 1 to provide:
  • ⁇ overscore ( ⁇ ) ⁇ 1 [a 1 T a 1 ] ⁇ 1 a 1 T ⁇ 1 ⁇ overscore ( ⁇ ) ⁇ 1 22b.
  • ⁇ overscore ( ⁇ ) ⁇ 1 where a 1 , ⁇ 1 and ⁇ overscore ( ⁇ ) ⁇ 1 have been defined above.
  • ⁇ [ a 1 T ⁇ a 2 T ] ⁇ [ a 1 a 2 ] ⁇ ⁇ ⁇ _ 2 [ a 1 T ⁇ a 2 t ] ⁇ [ ⁇ 1 ⁇ ⁇ _ 1 ⁇ 2 ⁇ ⁇ _ 2 ] 26.
  • ⁇ ⁇ Roll n tan - 1 ⁇ ( ⁇ n ( 2 ) ⁇ n ( 1 ) ) .
  • the heading and pitch might be approximated from the ground track (arctan Vn/Ve), and the pitch from the flight path angle (arctan of the vertical velocity or rate of change of altitude and the ground speed as determined from delta P North and delta P east).
  • a rough heading may be available from a magnetic compass or a solid state magnetic compass available from Honeywell. If the winds aloft are known, they might be used to correct the heading and if the angle of attack were known, it might be used to correct the pitch angle.
  • FIG. 5 is a block diagram that schematically provides an overview of the process functions necessary for roll angle computation.
  • GPS RECEIVER, block 500 is shown with its internal computer providing POSITION and VELOCITY data via POSITION sampler 502 , and VELOCITY SAMPLER 504 .
  • Each sampler has a respective sampler delay 506 and 508 .
  • the outputs of the samplers are A POSITION and ⁇ VELOCITY and this data is coupled to a ROLL ESTIMATE (Iterative Solution) functional block 510 .
  • the ACCELEROMETERS block 512 represents the triax of accelerometers aligned with the BODY AXES described earlier.
  • the component of acceleration a x is aligned with the longitudinal axis of the projectile as shown in Figure The component of acceleration a x changes very slowly during the flight from one second to the next.
  • the component of acceleration a y is the cross track acceleration and the a z is the component of acceleration along the up axis both being shown in FIG. 1 .
  • the PITCH HEADING COEFFICIENT MATRIX 514 is initialized with ay and az accelerometer data. Processing of the data uses present PITCH ESTIMATE and HEADING ESTIMATE for trigonometric values.
  • the input ⁇ T will be shown to have the preferred value of one second.
  • the PITCH HEADING COEFFICIENT MATRIX is used with the GPS A POSITION and ⁇ VELOCITY inputs by the ROLL ESTIMATE functional block 510 to provide a roll angle ⁇ output to the FLIGHT CONTROL block 516 which includes block 26 in FIG. 1 .
  • the smoothing process referred to by block 344 in FIG. 3a will now be explained in connection with a discussion of FIGS. 6, 7 a and 7 b .
  • the invention projectile guidance system with accelerometers and a GPS receiver outputs a smoothed estimate of the past trajectory of the projectile from launch to its present position, throughout its flight, to the FLIGHT CONTROL block 26 , shown on FIGS. 1 and 5, along with the attitude angles to permit the flight control function 26 to adjust the heading or ground track of the projectile to the known target location.
  • FIG. 6 provides an embodiment of a forward smoother.
  • the embodiment shown uses Kalman filter.
  • the Kalman filter of block 364 , on FIG. 3 b is such a filter in which there have been n measurements ⁇ y 1 , y 2 , y 2 . . . , y n ⁇ at times t 1 t 2 , . . . , t n .
  • a measurement at time t k might contain acceleration data from an instrument or a velocity or a piece of position data or a sample of velocity or position data from a GPS input or from accelerometer data as delta V data and these values are arrayed as values of the y vector as ⁇ y 1 , y 2 , y 2 , . . . , y n ⁇ .
  • the process is time indexed or sample indexed with GPS information at a one Hz sample rate. Between GPS samples, the system reprocesses all past samples and states using the measurement index counter or k counter to provide an index as it counts from 1 to n.
  • Measurement data such as GPS position data, is indexed as it is acquired or received as samples 1 through k with the last sample received being measurements indexed as sample n.
  • Block 602 shows that the sample index counter, the k counter, is then set to one and block 604 tests to see if time t is greater than t n . If time is less than or equal to t n , the test advances to block 606 and increments the index counter by one.
  • Block 608 represents the step of propagating the system state vector or estimated state vector x from time t k ⁇ 1 to time ⁇ k ⁇ 1 .
  • the symbol ⁇ k ⁇ 1 represents the system equation or transfer function.
  • the transfer function ⁇ k ⁇ 1 propagates the state vector of the system x from time k ⁇ 1 to time k.
  • the state vector expressed as a state matrix “x” is a column matrix that is “m” by one in dimension.
  • the covariance matrix P is “m” by “m” in dimension.
  • P k is the error covariance associated with the filter estimate of the state vector x ⁇ overscore (k) ⁇ .
  • the transfer function ⁇ k ⁇ 1 and its transpose ⁇ k ⁇ 1 T are introduced above.
  • Q k ⁇ 1 is the covariance matrix of the process noise.
  • the symbol G k represents the Kalman gain.
  • the measurement matrix will typically be formed from elements such as Vx, Vy.
  • the y vector or measurement vector is formed from the product of the H matrix and the state vector x the product being added to the measurement noise matrix.
  • the error covariance matrix P ⁇ overscore (k) ⁇ is multiplied by the transpose of the measurement matrix H k T .
  • the product of the two is then multiplied by the measurement matrix H k .
  • the result of the product is added to R k , the covariance matrix of the measurement noise vector.
  • the R k matrix is obtained from information that is gathered by the systems engineers through empirical testing.
  • the systems engineers determine what noise is associated with each sensor by collecting historical noise data on each measurement variable.
  • the H k matrix is given and is hardware and instrument dependent.
  • the Kalman gain is determined and then used to update the estimate of the state vectors in block 614 .
  • ⁇ circumflex over (x) ⁇ k ⁇ circumflex over (x) ⁇ ⁇ overscore (k) ⁇ +G k [yk ⁇ Hk ⁇ circumflex over (x) ⁇ ⁇ overscore (k) ⁇ ].
  • H k multiplies the term ⁇ circumflex over (x) ⁇ ⁇ overscore (K) ⁇ .
  • the result is subtracted from Yk.
  • the result is an observable difference that is multiplied by the Kalman gain and then added to the previously estimated state vector ⁇ circumflex over (x) ⁇ ⁇ overscore (K) ⁇ .
  • the minus sign in the superscript of ⁇ circumflex over (x) ⁇ ⁇ overscore (K) ⁇ implies that it represents the state a little before the kth update.
  • the sample index “k” can range in value from 1 to n where n is the most recent update index in time.
  • a state variable without a superscript implies that the state variable value is a value that exists just after an update.
  • the symbol ⁇ circumflex over (x) ⁇ overscore (K) ⁇ represents the kth estimate of the state vector x.
  • the measurement index “k” is a running index.
  • the matrix 1 is an identity matrix. All of its elements are zero except the main diagonal elements which are nes. The dimension of the identity matrix is matched to the product of G k and H k matrices. All of the values necessary for the computation of the covariance matrix are available from previous steps.
  • the process leaves block 616 and transfers back to decision block 604 to once again test to see if t>t n . As time reaches t n , all of the measurements have been processed. No additional measurements are to be made. A “yes” result transfers the process to the Scenario Complete block 618 and the mission is completed. If the flight had lasted one hundred seconds and the GPS provided position measurements at one per second, there would have been 100 GPS samples and the sample index k would have been incremented from 1 to 100. The index “k” can not exceed 100.
  • FIGS. 7 a and 7 b form a fixed interval smoother, FIG. 7 a providing a forward pass and FIG. 7 b providing a backward pass.
  • FIG. 7 a can be seen to be identical in function to that of FIG. 6 with the exception of blocks 700 .
  • the process exits block and advances to block 702 also found at the top of FIG. 7 b .
  • the backward sweep begins with block 704 as the process sets the sample index counter, i.e., the k counter to current index value of n.
  • k) means that the matrix will be evaluated for all measurements up to and including the kth measurement.
  • the backward sweep begins only after the conclusion of a forward sweep. All k measurements are available at the conclusion of the forward sweep. All k data points form a fixed interval, and all n measurements from t k back to t 1 are used during the backward sweep.
  • the rightmost term in block 706 is the inverse of the covariance matrix P(k+1
  • the vertical bar followed by “k” shows that all of the data for measurements through k is to be used.
  • the process then advances to block 708 .
  • the object of the equation in block 708 is to compute a smoothed state vector ⁇ circumflex over (x) ⁇ (k
  • the equation in block 708 is:
  • n ) ⁇ circumflex over (x) ⁇ ( k
  • the gain matrix A(k is available from block 706 .
  • the first term after the equal sign is the kth state vector estimate using measurement data through measurement k.
  • the first term inside of the bracket the term ⁇ circumflex over (x) ⁇ (k+1
  • k) is an estimate of the state vector at time k+1 using all measurements up to time t k .
  • the difference is calculated as the second term is subtracted from the first.
  • the result is multiplied by the gain matrix, the product is added to ⁇ circumflex over (x) ⁇ (k
  • k) uses all data through the kth update.
  • n) uses all of the data from measurements through measurement n.
  • k) uses only data up though the kth update.
  • a covariance difference is calculated from the covariance terms within the brackets.
  • the covariance difference term is then multiplied by the gain matrix and the result is added to P(k

Abstract

A projectile guidance system without gyros in which the projectile has an orthogonal body cordinate system. The projectile has a triax of accelerometers providing x, y and z acceleration data measured along the x, y and z axes respectively. A GPS antenna and receiver means provides onboard GPS position and velocity data in earth referenced navigational coordinates. A computer and program means stores and accesses time indexed GPS position and GPS velocity data and transforms x, y and z axis acceleration data from body to navigation coordinates. The program means is responsive to corresponding time indexed acceleration data and to GPS velocity and position data for calculating and outputing an estimated-projectile roll, pitch and yaw angle via optimal smoothing techniques with respect to local level for each time index iteration of present position to a flight control system for guiding the projectile to a predetermined location.

Description

FIELD OF THE INVENTION
This invention relates to the field of aircraft or projectile attitude determination and estimation using a GPS signal; the system using a first and second linear accelerometer for an estimation of the projectile's roll angle, and information from an additional third accelerometer for a pitch angle estimation; the system further including means for detecting and avoiding the effects of GPS signal jamming.
BACKGROUND
The general problem to be solved is how to guide a gun-fired projectile onto a target with a known geographic location at lowest cost with reasonable reliability. This application addresses a portion of that problem by providing an estimate of the trajectory of the projectile from launch, the initial conditions of the projectile immediately after launch and the distance, direction and altitude to the idealized trajectory calculated for the projectile at the time of launch or firing and by reliably detecting and avoiding the effects of GPS signal jamming.
A first approach to the problem to be solved used only a GPS receiver and a turns counter. Although such a system represents a relatively inexpensive solution, it may be vulnerable to GPS jamming. Accordingly, additional measures may need to be implemented to ensure reliable reception and processing of an uncorrupted GPS signal, e.g., protection of the GPS signal.
A second approach used a GPS receiver, a turns counter, and a triax of gyros, which adds to the cost of the approach. Similarly to the first approach, this second approach requires protection of the GPS signal almost all the way into the target. As in the first approach, such protection is required because, in the event the GPS signal is lost, no mechanism exists to account for any external forces that may act on the projectile throughout its flight. Accordingly, a need exists for a system and process for guiding a projectile to a target while minimizing or eliminating the vulnerability of the system and process to interference with, e.g., jamming of, the GPS signal.
Prior attempts to meet this need have focused on either preventing interference with the GPS signal or enabling operation with limited GPS data. Attempts to enable operation with limited GPS data have typically involved increasing the performance and/or functionality of the inertial instruments on board the projectile. For example, to address the inability of the above-mentioned second approach to account for the projectile's reaction to external forces if/when the GPS signal may be lost, additional accelerometers may be incorporated into the system to enable compensation for the projectile's reaction to external forces, i.e., the sensor package may comprise a complete IMU. Gyroscopic instruments for aircraft use arc well known and available in a number of technologies such as iron rotor and tuned rotor gyros, ring laser gyros, multi-oscillator gyros, zero lock gyros (ZLG), fiber optic gyros, resonator gyros such as HRGs or hemispherical or tubular ceramic resonant gyros and the like.
Unfortunately, however, incorporation of additional gyroscopic instruments and/or accelerometers are considered much too costly because of the gyros already in the package. Moreover, use of such instruments imposes additional constraints on the operational envelopes of the projectiles. For example, gyroscopic instruments are typically subject to failure modes and uncertainties relating to launch accelerations in the range of 15,000-30,000 Gs. Further, use of these technologies usually requires that the vehicle carry at least one gyro in a gimbaled or strap-down arrangement with the attendant disadvantages of cost, weight and power dissipation.
Accordingly, it would be advantageous to have an improved, cost-effective system and process for providing projectile guidance in the presence of GPS signal jamming and/or with limited GPS data.
SUMMARY
In accordance with a first exemplary embodiment of the invention system and process a projectile without gyros is guided toward a target using a GPS signal and a triax of accelerometers. A computer-implemented process uses GPS position and GPS delta velocity data along with data from-the accelerometer triax to determine the projectile's estimated attitude in pitch, roll and yaw. With the projectile's position known from data provided by the GPS signal received by a GPS receiver, the computer-implemented process determines the projectile's attitude in navigational coordinates and creates a time indexed record of the projectile's trajectory after the on-board GPS receiver locks on to the required number of satellites. The data in the time indexed record of the trajectory is filtered and smoothed. As the projectile rolls, the accelerometers are used to measure the forces acting on the projectile and the projectile's rotation rates. In some alternative embodiments of the invention, the GPS is used to provide data for the calculation of initial aiming and velocity errors and for the calibration of the accelerometers when positioned in the gun barrel prior to launch.
It should be noted that the cost associated with this approach depends largely upon the accuracy of the accelerometers that must be used, which depends upon the required delivery accuracy of the projectile. Where cost must be reduced, lower accuracy accelerometers can be used with a greater reliance on GPS signal data after launch. Therefore, to reduce cost while retaining reasonable levels of projectile delivery accuracy, greater reliance is placed on GPS signal data. Thus, an aspect of the present invention provides for improved reliability of GPS signals.
In an exemplary embodiment, GPS signal data may be acquired from GPS signals transmitted from one or more satellites and received by one or more antennas on the projectile. Where the potential exists to encounter jamming of one or more of the GPS signals, one or more corresponding GPS signal jamming detector may be included to monitor each GPS signal and to detect whether each GPS signal has been subjected to jamming. If such jamming is detected, an anti-jammer will implement GPS signal protection measures.
Exemplary GPS signal protection measures may include causing the projectile to engage, or remain engaged, in a periodic motion, e.g., rolling, and using the periodic motion of the projectile to selectively sample GPS signals in such a manner as to detect and omit jammed GPS signals and to enable reliable processing of unjammed signals, e.g., by selectively and periodically avoid GPS signals that exhibit jamming. It should be noted that as a projectile proceeds through each cycle of its periodic motion, i.e., each rolling revolution, each of the one or more antennas will periodically be positioned to receive a GPS signal from each of the one or more satellites. Thus, so long as at least one GPS signal from a satellite remains capable of being received by an antenna in an unjammed condition, each of the one or more antennas will periodically be free from jamming, e.g., during at least a portion of the roll attitude.
Alternatively, where the projectile motion permits one or more antenna to remain oriented so as to continuously receive an unjammed GPS signal, such as where the projectile is not spinning, exemplary GPS signal protection measures may include detecting whether a GPS signal received by one or more of the antennas is free from jamming and switching a GPS receiver to use only the unjammed signals. It should be noted that in such an exemplary embodiment, the projectile need not be spinning or rolling. Accordingly, this protection measure may be implemented with projectiles that are not roll-stabilized. It should also be noted that, in accordance with this embodiment, the antenna(s) may be decoupled from the main body of the projectile via a mechanism such as a slip ring. Accordingly, the projectile may be spinning or roll stabilized while the antennas are maintained in a fixed orientation with respect to one or more satellites. Similarly, the projectile may be stationary while the antennas undergo periodic motion, e.g., spinning, with respect to one or more satellites.
Other exemplary protection measures may include conversion of the GPS signal from an RF signal to a digital signal as well as implementation of an automatic gain control. In such embodiments, each GPS signal may be converted by a high speed analog to digital converter immediately, or very soon, after it is received. In addition, the converted digital GPS signal may be passed through a digitally implemented automatic gain control circuit. Both the analog to digital converter and the automatic gain control circuit may be implemented in the GPS radio receiver.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective and exploded view of a projectile or unmanned airborne device equipped with an on-board GPS receiver, a set of accelerometers coupled to a vehicle frame, a plurality of antennas, and on-board computer cards for executing the invention process;
FIG. 2 shows a launch vehicle and a desired trajectory with a flight error envelope region around the trajectory;
FIGS. 3a, 3 b, 3 c and 3 d each show a block diagram for processing accelerometer and GPS data for the purpose of estimating the trajectory of flight;
FIG. 4 is a perspective schematic view of an aircraft showing a typical coordinate system and defining angles of rotation;
FIG. 5 is a block diagram for the functional steps in a Roll Angle Computation;
FIG. 6 is a flow chart for the steps in a typical Kalman filter and for calculating an alternate roll angle;
FIG. 7a is a flow chart of the forward filter steps in a typical smoother;
FIG. 7b is a flow chart of the backward filter steps in a typical smoother; and
FIG. 8 illustrates time dependent GPS signals as received by a plurality of antennas on a rotating projectile in the presence of GPS signal jamming.
DISCLOSURE OF THE INVENTION
FIG. 1 schematically shows the major components in an exemplary embodiment of a projectile guidance system without gyros 10distributed in the exploded perspective view of a projectile 12. The projectile 12 is depicted in flight after having been fired from a gun (not shown).
The projectile is shown having an orthogonal body fixed coordinate system. The rotation rate components in roll φ, with a longitudinal axis Xb, a pitch axis Yb and a yaw axis zb. FIG. 4 shows an aircraft with a corresponding orthogonal body coordinate system. The rotation rate components in roll φ, pitch θ and yaw φ are defined in FIG. 4. A locally level fixed earth navigational coordinate system is also depicted in FIG. 4. When the wander angle is zero, the YN axis is typically parallel to a meridian of longitude and points true north. The XN axis is parallel to a parallel of latitude and points east and the ZN axis extends from the surface of the earth as a gravity vector. The angle a is used in a navigation system to traverse the poles of the earth without encountering position singularities. In operation, components of time indexed data elements such as projectile acceleration and velocity are transformed from the body coordinates, indicated by a subscript “b” into the earth referenced coordinate data elements indicated by a subscript N using conventional direction cosine matrices.
Referring again to FIG. 1, the projectile, guided by the projectile guidance system without gyros, has a triax of accelerometers 14. The triax has an x-axis accelerometer for providing x-axis acceleration data measured along the xb axis, a y-axis-accelerometer for providing y-axis acceleration data measured along the Yb axis and a z-axis accelerometer for providing z-axis acceleration data measured along the zb axis. A GPS antenna represented by band 16 and a GPS receiver represented by module 18, in combination, represent a means for providing onboard GPS position and altitude and GPS velocity data in earth referenced navigational coordinates. Alternative antenna patterns 88, 89 are configured to receive GPS data from one or more satellite 78, 79. While only antenna patterns 88, 89 and antenna band 16 are shown, it should be noted that any number, configuration, and/or orientation of antennas may be included on the projectile, each antenna being configured and oriented to receive GPS signals from a different direction or range of directions (e.g., each antenna pattern having a lobe directed toward a different direction or range of directions). Similarly, although only one GPS receiver 18 is shown, it should be noted that a plurality of GPS receivers may be implemented to accommodate processing of the GPS signals received through the specific number, configuration and orientation of antennas implemented on the projectile.
Module 20 represents a guidance processor which provides the function of a computer, memory and program means for storing and accessing time indexed GPS position and GPS velocity data, for implementing GPS signal protection measures as described herein, and for transforming the x, y and z axis acceleration data from body to navigation coordinates. The acceleration data is arrayed and has time indexes that are common with the time indexes for the GPS position and velocity data. A turns counter 22 provides an ac signal in flight representing the angular rate of rotation of the projectile in the earth's magnetic field.
The computer, memory and program means on module 20 receives and responds to corresponding time indexed acceleration data, GPS velocity and position data for calculating and outputing corresponding sets of time indexed estimates of the projectile roll, pitch and yaw angles with respect to the locally level earth referenced navigation coordinates for each time index iteration of the program to provide present position, velocity and acceleration data to a flight control and ballistic data system represented by module 26 for it to use in guiding the projectile to a predetermined target location.
The flight control and ballistic data system controls the projectile by providing commands to control surfaces such as canards 28, 30 to keep the projectile on a trajectory to the target location. The selection and or design of a flight control and ballistic data system represented by card or module 26 is believed to be a design choice and is not the subject of this invention disclosure. Nevertheless, if the projectile is engaged in periodic motion, e.g., rolling, the present invention provides that trajectory corrections may be made by waiting for an orientation of a control surface to correspond with a direction in which it is desirable to steer the projectile.
The present invention also contemplates that if the trajectory corrections are large and the projectile guidance section is roll stabilized, then the projectile can be de-spun and the corrections made while the projectile is in a roll-stabilized mode. Then, after completing the corrections, the projectile can go back to being a rolling airframe. The present invention enables these capabilities by providing a mechanism for determining the roll orientation of the projectile. For example, with reference to FIG. 3c, the roll orientation of the projectile may be determined through: 1) a roll gyro, 2) the roll position of GPS satellites as they turn on/off, 3) GPS attitude determination with multi antennas, and 4) a magnetic turns counter.
In accordance with an exemplary embodiment, GPS signal data may acquired from GPS signals transmitted from one or more satellites 78, 79 and received by one or more antennas 88, 89 on the projectile. With further reference to FIG. 3c, in an exemplary embodiment, a plurality of GPS antenna patterns 88, 89 receive GPS signals which are passed through RF processing means 98, 99 to produce RF processed GPS signal 3344. Information from a high speed correlator 3354, and roll reference 3364 are transmitted to processor 3375 along with RF processed GPS signal 3344. Based on signals 3344, 3354, and 3364, processor 3374 produces a position signal 3381, a velocity signal 3382, and an attitude signal 3383.
As shown in FIG. 3d, each GPS signal 3407 may be sent through a low noise amplifier 3417 before being received by radio 3427. Also, in an exemplary embodiment, one or more GPS signal jamming detectors 3418 may be included to monitor each GPS signal 3407 and to detect whether each GPS signal has been subjected to jamming. If such jamming is detected, an anti-jammer 3419 may implement GPS signal protection measures which may, for example, selectively and periodically avoid GPS signals that exhibit jamming based on the periodic motion of the antenna portion of the projectile. As shown in FIG. 3d, jamming detector 3418 and anti-jammer 3419 transmit signals to system processor 3457, which also receives information from roll reference 3467 and GPS receiver 3437. Based on signals received from system processor 3457, digital filters 3427 receive GPS signals from radio 3427 and selectively transmit unjammed portions of those GPS signals to GPS receiver 3437. GPS receiver 3437 then uses pre-stored data 3447 to process and transmit GPS signals to system processor 3457. Finally, system processor 3457 utilizes roll reference 3467 and GPS signal to transmit signals to autopilot 3477, which causes control surfaces 3487 to be actuated, thereby guiding the projectile to a target.
In an exemplary embodiment, a GPS signal protection measure involves causing the projectile to engage, or remain engaged, in a periodic motion (e.g., spinning, rolling, or otherwise oscillating) and using the periodic motion of the projectile to selectively sample GPS signals in such a manner as to detect and omit jammed GPS signals and to enable reliable processing of unjammed signals. It should be noted that as a projectile proceeds through each cycle of its periodic motion (i.e., through each rolling or spinning revolution, oscillation, or other periodic motion) each of the one or more antennas 88, 89 will periodically be positioned to receive a GPS signal from each of the one or more satellites 78, 79. Thus, so long as at least one GPS signal from a satellite remains capable of being received in an unjammed state by one or more antenna, each of the one or more antennas will periodically be free from jamming, e.g., during at least a portion of the roll attitude.
FIG. 8 illustrates three exemplary time-dependent GPS signals as received by three corresponding GPS antenna and receiver means implemented on a projectile undergoing periodic motion, e.g., spinning. As shown in FIG. 8, a first GPS signal exhibits jamming as the projectile rotates through an orientation from approximately 30 degrees to an orientation of approximately 210 degrees. Similarly, a second GPS signal exhibits jamming as the projectile rotates through an orientation from approximately 120 degrees to an orientation of approximately 360 degrees. Finally, a third GPS signal exhibits jamming as the projectile rotates through an orientation from approximately 360 degrees to an orientation of approximately 30 degrees. Accordingly, an substantially continuous unjammed GPS signal may be received by switching on the first antenna as the projectile rotates between approximately 210 degrees and approximately 30 degrees, by switching on the second antenna as the projectile rotates between approximately 360 degrees and approximately 120 degrees, by switching on the third antenna as the projectile rotates between approximately 30 degrees and approximately 360 degrees, by switching off the first antenna as the projectile rotates between approximately 30 degrees and approximately 210 degrees, by switching off the second antenna as the projectile rotates between approximately 120 degrees and approximately 360 degrees, and by switching off the third antenna as the projectile rotates between approximately 360 degrees and approximately 30 degrees.
With further reference to FIG. 1, in one embodiment, the flight control and ballistic data system 26 is pre-programmed to use information provided via bus 32 from the projectile guidance system without gyros 12, after launch, to de-spin the projectile and to roughly position the top of the projectile skyward, or to otherwise orient an antenna pattern 88, 89, so as to optimize the reception of GPS signals. In accordance with this embodiment, after the projectile is de-spun, the accelerometers are un-caged and activated. The computer, memory and program means then performs its first estimate and update of the state matrix including an estimate of the vehicle rates. In accordance with this exemplary embodiment, where the projectile motion is such that it may permit one or more antenna 88, 89 to remain oriented so as to continuously receive an unjammed GPS signal, the anti-jammer 3419 may detect that a GPS signal 3407 received by one or more of the antennas is free from jamming and may switch or otherwise cause the one or more GPS receiver 18 to use only the unjammed signal. It should be noted that in such an exemplary embodiment, an unjammed GPS signal may be received without requiring the projectile to be rolled. To accomplish this, a computer-implemented process may be implemented as a guidance program configured to cause the projectile to maintain an orientation of the GPS antenna and receiver means so as to permit one or more antenna to substantially continuously receive an unjammed GPS signal.
It should be noted that in such an exemplary embodiment, the projectile need not be spinning or rolling. Accordingly, this protection measure may be implemented with projectiles that are not roll-stabilized. It should also be noted that, in accordance with this embodiment, the antenna(s) may be decoupled from the main body of the projectile via a mechanism such as a slip ring. Accordingly, the projectile may be spinning or roll stabilized while the antennas are maintained in a fixed orientation with respect to one or more satellites. Similarly, the projectile may be stationary while the antennas undergo periodic motion, e.g., spinning, with respect to one or more satellites.
Thus, in accordance with the invention, the projectile may either be spinning or roll stabilized, e.g., by decoupling it from the main body of the projectile via a slip ring. In the event no unjammed GPS signal may be substantially continuously received, the anti-jamming means may be configured to cause the projectile to engage in a periodic motion and to selectively and periodically avoid GPS signals that exhibit jamming.
Other exemplary protection measures may include immediate conversion of the GPS signal from an RF signal to a digital signal as well as implementation of an automatic gain control. In such embodiments, each GPS signal may be converted immediately or very soon after it is received by a high speed analog to digital converter. Then, the digital GPS signal may pass through a digitally implemented automatic gain control circuit. Both the analog to digital converter and the automatic gain control circuit may be implemented in the GPS radio receiver.
In an exemplary embodiment, the system may be configured to be initialized prior to firing. In accordance with this embodiment, prior to projectile firing, the system may determine and store in memory which satellites will be in the field-of-view (FOV) of each antenna pattern 88, 89 throughout the trajectory of the projectile and which combination of satellites 78, 79 gives the best GDOP for the trajectory. This information is pre-stored in the receiver 18 along with any other correction data that may be available.
In an exemplary embodiment, as shown in FIG. 3d, the GPS signals 3407 are transmitted through a low noise amplifier 3417 to a radio receiver 3427, which may comprise a high speed analog to digital converter (e.g., a 5 gigabit/second analog to digital converter with 14 bits of resolution). Radio receiver 3427 may also comprise a digitally implemented automatic gain control circuit. The signals are then sent to a set of digital filters 3427 as well as one or more jamming detector 3418. It should be noted that a separate filter 3427 may be implemented for each pre-selected satellite 78, 79 that will be used in the TOA computation. It should also be noted that digital filters 3427 may be dynamically tuned in real time to band pass the frequency of each pre-selected satellite. The center of the band pass will be the GPS carrier frequency adjusted for Doppler motion between the projectile and the satellite. The GPS signals are then sent to the GPS receiver 3437 where they are correlated against the known code of each of the pre-selected satellites via a high speed digital correlator 3447, and position and velocity determined.
If the vehicle is rolling, then rate information is extracted by separating the accelerometer ac signal from the dc or steady state signal. As the projectile rolls, the pitch and yaw accelerometers output signals will vary as a sine wave function. If the vehicle is not rolling, then data is extracted and transferred from the body coordinate system to the earth referenced navigation coordinate system using DCM (direction cosine matrix) relationships as required.
FIG. 2 shows a mobile artillery weapon, firing a projectile toward a target. In the equation shown, {right arrow over (X)}(t)True is a vector quantity representing the computed true position of the projectile as a function of time. {right arrow over (X)}(t)Nominal is a vector representing the ideal location of the projectile on the ideal trajectory. {right arrow over (X)}(0)Error is a vector representing the position error of the projectile at time zero before launch. {right arrow over (X)}(t)Error is a vector representing the error in the projectiles position due to accumulated errors resulting from navigational instrument error and GPS errors. The figure shows the sequence of events and schematically portrays an error budget region in dashed lines that concludes with an ellipse representing the TARGET ERROR that can result from launching the projectile using conventional artillery practice with no on board guidance.
The funnel region in a continuous line schematically shows the position error of an on-board GPS progressively diminishing and asymptotically approaching a limit that is much smaller than the TARGET ERROR limit for a trajectory with no on board guidance. The invention projectile guidance system without gyros 10 uses a triad of accelerometers to provide real time body referenced data to a computer, memory and program means and real time position data from a GPS to establish and output the attitude of the projectile. The outputs are Kalman filtered and coupled to the flight control and ballistic data system represented by module 26 shown in FIG. 1 along with the aiding GPS position data for use in steering the projectile into the region bounded by the funnel region.
FIGS. 3a and 3 b schematically show an embodiment of a data flow used by the projectile guidance system without gyros 10. Phantom block 300 represents the function provided by a fire control and ballistics computer as it executes an initialization program to process data received from data sources such as an external input of a TARGET LOCATION, the geographic location of the weapon launching the projectile, the PROJECTILE TYPE, the PITCH ALIGNMENT IN BARREL, the pitch angle of the launching tube, the outputs of the triax 304 of three components of acceleration ax, ay and az, in body coordinates, the roll angle ROLL φ, and the roll rate ROLL RATE φ from the spin counter 308. The FIRE CONTROL AND BALLISTICS computer processes the data available and prior to launch transfers the initial state data such the initial orientation angles, body fixed angle rates, present position and initial velocity components. The spin counter 308 and the triax 304 provide their outputs directly to the INITIAL PROJECTILE STATE ESTIMATE 312 via signal paths 314 and 333 respectively. It is most likely that all initial conditions would be input into the projectile from an external source such as the FIRE CONTROL AND BALLISTICS function 302 via an electrical, magnetic or optical link, or perhaps mechanical link. If the gun were to be mounted on a ship, the initial conditions would have to be extended to include data such as the ship's velocity, heading, displacement from the ship's inertial guidance computer, and possibly the coordinates of the gun with respect to the station from which the gun is receiving its initial condition information.
The FIRE CONTROL AND BALLISTICS function 302 also provides roll indexing information to the spin counter 308 to provide a zero reference. The spin counter 308 provides estimates of roll angle φb to an accuracy of a few degrees, as well as roll rate φb the FIRE CONTROL AND BALLISTICS function 302 precomputes an expected ballistic trajectory which is also passed to the projectile. This ballistic information, along with accelerometer information, or data directly from the FIRE CONTROL AND BALLISTICS function 302 is used to determine the initial state vector and attitudes of the projectile at initialization of the estimation process. The algorithm is initialized when both the accelerometer and the GPS data are available for state estimation. The FIRE CONTROL AND BALLISTICS function 302 also receives a set of initial states for orientation and position of the projectile via signal path 320 from the ESTIMATION OF NEW INITIAL TARGET STATE function 322 as a result of a failure of a fit test.
The FIRE CONTROL AND BALLISTICS function 302 outputs a set of initial STATE ESTIMATES to the INITIAL PROJECTILE STATE ESTIMATE functional block 312 which transfers initial BODY STATE ESTIMATES {right arrow over (V)}0, {right arrow over (x)}0 via signal path 324 to SMOOTHING PROCESS function block 344 and a set of ATTITUDE STATE ESTIMATES via signal path 330 to the initial state estimate of the initial attitude angle array in ATTITUDE FILE 332.
The turns or SPIN COUNTER 308 which provided turn count data to the FIRE CONTROL AND BALLISTICS function 302 also provides turn count data via signal line 333 to the INITIAL PROJECTILE STATE ESTIMATE FUNCTION block 312 and to the time indexed SPIN COUNTER MEASURED DATA memory array represented on FIG. 3b by functional block 350 where the total roll angle φ(n) of the projectile is accumulated and time indexed and transferred via path 351 to the ATTITUDE ESTIMATION ALGORITHM 372. Spin counter technology is a mature technology. The Alliant Techsystems company has reportedly developed one small enough to fit into a 20 mm projectile. A turns counter for larger diameter projectiles is therefore a product that can be purchased for use in the invention system and process without difficulty. The output of the turns counter is a sine wave output as the projectile rotates through the Earth's Magnetic Field.
The INITIAL PROJECTILE STATE ESTIMATE FUNCTION block 312 provides initial ATTITUDE STATE ESTIMATE values for azimuth φ0, pitch θ0 and roll φ0 angle to the ATTITUDE FILE 332 in FIG. 3b as initial values.
The outputs of the triax 304 of three components of acceleration ax ay and az in body coordinates are processed by the function represented by the block 336 to transfer time indexed body referenced changes in velocity via signal path 338 to the ACCEL DATA FILE memory array 340. The ACCEL DATA FILE memory array 340 couples an array of time indexed acceleration data elements to the SMOOTHING PROCESS function block 344.
The filtering and smoothing process of block 344 will be discussed in connection with FIGS. 6, 7 a and 7 b later in this disclosure. The smoothing process uses the initial estimates of attitude, velocity and position in conjunction with the present accelerometer data to determine velocity and position of the projectile in body coordinates. The output of the smoothing process are STATE VECTOR ESTIMATES, {right arrow over (X)}B(n), {right arrow over (V)}B(n) for position and velocity which are coupled via signal path 346 to the BODY TO INERTIAL TRANSFORMATION functional block 348.
The GPS MEASURED DATA function block 356 periodically receives time indexed velocity and position data {right arrow over (V)}(n) and {right arrow over (X)}(n) and transfers the data via signal path 358 into the time indexed array in the computer, memory and program means memory shown as function block 360. The GPS velocity and position data is transferred via signal path 362 to a Kalman filter represented by function block 364. The Kalman filter transfers filtered values of the projectile's estimated present position and velocity vectors via signal path 368 to the FIT ERROR TEST functional block 370 and to the ATTITUDE ESTIMATION ALGORITHM functional block 372. The ATTITUDE FILE 332 transfers time indexed estimated attitude angles and attitude angular rate data to the ATTITUDE ESTIMATION ALGORITHM functional block 372 via signal path 374 and to the BALLISTICS ESTIMATE (n) functional block 376 via transfer path 378 in earth referenced navigational coordinates. The BALLISTIC ESTIMATES uses the known model characteristics of the projectile with the corrected initial position and initial velocity information via path 375 and the history of all past attitude and attitude rates from path 378 to provide a modeled estimate of the present position and velocity via path 382 to the ATTITUDE ESTIMATION ALGORITHM 372.
The filtered body STATE VECTOR ESTIMATES {right arrow over ({circumflex over (X)})}B(n), {right arrow over ({circumflex over (V)})}B(n) vectors in the orthogonal body coordinate system, are transferred via signal path 346 to the BODY TO INERTIAL TRANSFORMATION block 348. The BODY TO INERTIAL TRANSFORMATION block 348 receives the estimated attitude angles and attitude angular via signal paths 384 and 386 and processes the STATE VECTOR ESTIMATES from representation in the orthogonal body coordinate system into vectors in the earth referenced navigational coordinate system to position and velocity estimates in earth referenced navigational coordinates using conventional direction cosine transformations such as those explained in the text by George Siouris, titled “Aerospace Avionics Systems, A Modern Synthesis”, published by Academic Press, published in 1993. This estimation process can be simplified and improved using measured turns counter data and by computing a new ballistic trajectory based on new initial state information.
The BODY TO INERTIAL TRANSFORMATION functional block 348 outputs the estimated position and velocity STATE VECTOR ESTIMATES in earth referenced navigational coordinates via signal path 388 to the FIT ERROR TEST functional block 370 where the STATE VECTOR ESTIMATES are compared to the Kalman filtered GPS position and velocity. It is not possible in a statistical sense to make the estimation process fit better than the GPS position and the errors associated with the GPS. If the error for the differences between the two state vectors is less than 1 or 2 times the GPS error, the algorithm declares the fit to be “statistically good enough” to quit and wait for a new measured data point to arrive. If the test passes, the estimates of position, velocity, attitude and attitude rates are used to update the n−1 position in the estimated position and attitude time indexed memory arrays.
If the test fails, the algorithm estimates a new set of initial projectile states via a perturbation algorithm and repeats the estimation process again, until the solution converges to limits within the predetermined fit error criteria. If the test fails, a FAIL signal is coupled via path 390 to the ESTIMATION OF NEW INITIAL TARTET STATE functional block 322 which adjusts the initial position, velocity, attitude and attitude rates and couples a modified set of estimated state data via signal path 320 into the INITIAL PROJECTILE STATE ESTIMATE functional block 312 for an additional cycle. Iteration continues until the initial conditions are adjusted to obtain a PASS signal out of functional block 370 followed by the next data iteration using GPS data one second later.
As discussed previously, in order to avoid excessive reliance on GPS and protection of the GPS signal, higher performing inertial instruments (e.g., inertial instruments performing at levels better than 100 micro g) may be used. Honeywell's VBA accelerometers and Silicon Accelerometer supplied from the Litton Guidance & Control Systems Div. of Northrop Grumman Inc. at Woodland Hills, Calif. 91637, the assignee, have such a capability.
A GPS Receiver by Alliant Techsystems is available for use in the invention system and process. The Alliant GPS uses a type 509 processor that has sufficient processing power and a separate memory which can be used to store user software and the system processor for this application. The Alliant receiver is configured with multiple RF front ends to accommodate multiple antenna inputs as a means of protecting the GPS signal as the projectile rolls. The GPS 509 processor can also be used to process the data and integrate the inertial data with the GPS and turns counter data. Software can be incorporated into the 509 processor to extract rate information from the accelerometer triax and integrate the data from the sensors.
Alternatively, where cost must be reduced, much lower accuracy accelerometers can be used with a greater reliance on GPS signal data after launch. As described above, in an exemplary embodiment, GPS signal data may acquired from GPS signals transmitted from one or more satellites 78, 79 and received by one or more antennas 88, 89 on the projectile. One or more GPS signal jamming detector 3418 may be included to monitor each GPS signal 3407 and to detect whether each GPS signal 3407 has been subjected to jamming. If such jamming is detected, an anti-jammer 3419 may implement GPS signal protection measures present in system processor 3457.
For example, anti-jammer 3419 may cause system processor 3457 to cause the projectile to engage, or remain engaged, in a periodic motion such as rolling or spinning. As the projectile proceeds through each cycle of the periodic motion, i.e., through each rolling revolution, each of the one or more antennas 88, 89 may periodically be positioned to receive a GPS signal from each of the one or more satellites 78, 79. Thus, so long as at least one GPS signal from a satellite remains capable of being by one or more antenna in an unjammed state, each of the one or more antennas will periodically be free from jamming, e.g., during at least a portion of the roll attitude.
Alternatively, where the jamming detector 3418 detects does not detect jamming in one or more GPS signal, anti-jammer 3419 may cause system processor 3457 to de-spin the projectile and to roughly position the top of the projectile skyward, or to otherwise orient an antenna pattern 88, 89, so as to optimize the reception of GPS signals 3407. In accordance with this embodiment, after the projectile is de-spun, the accelerometers are un-caged and activated. The computer, memory and program means then performs its first estimate and update of the state matrix including an estimate of the vehicle rates. In accordance with this exemplary embodiment, the anti-jammer 3419 may switch or otherwise cause the one or more GPS receiver 18 or the system processor 3457 to use only the unjammed GPS signal received by the one or more of the antennas that is free from jamming.
The roll angle of a guided projectile is typically provided by a gyro or a gyro platform. A roll angle signal characterizing the roll angle of the projectile is necessary to enable a flight control system to drive the flight control surfaces, such as canards, to roll the projectile to the left or right as required, to use lift from its lift surfaces to change the heading of the projectile to one directed to a target. It is an objective of this disclosure to provide a mathematical and therefore, a computer programmable process, for generating the roll angle of the projectile without signals from a gyro and by using the accelerometer outputs of a triax and the position and velocity signals from a GPS.
This technical description uses the following notation. {right arrow over (x)} denotes a vector with no specific reference frame of resolution. {right arrow over (x)}b denotes a vector resolved in a coordinate frame called the body-frame or projectile-frame. All coordinate frames discussed herein, including the body-frame coordinates, are right-handed orthogonal frames that have x, y, and z axes that extend from a location in the body of the projectile, such as the center of gravity, or origin designated as a reference point “O” to form an orthogonal triad extending in the forward or positive “Xb” axis direction, in the right or positive “yb” axis direction and down in the positive “Zb” axis directions. At least two accelerometers are fixed to and aligned with the body-frame along the y and zb axes. The principal axes of the b-frame coincide with the input axes of the inertial sensors and intersect at the origin “O”. A second coordinate frame of interest is the geographic or earth referenced navigational coordinate system or frame with principal axes X, Y and Z that coincide with the East, North, and Up directions as shown at the bottom of FIG. 4.
Subscripts on vectors are used to indicate a particular property or identification of the vector. Matrices are designated with capital letters. CN b denotes a direction cosine matrix (DCM) that transforms a vector from the N-frame or Navigation-frame to the body-frame, i.e., {right arrow over (x)}b=CN b {right arrow over (X)}N. Time dependency of a quantity is indicated with round brackets around a time variable or index. For example, CN b (t1) denotes the value of the DCM for the conversion from navigational to body-frame coordinates at time t1. The transpose of the CN b (t1) DCM provides Cb N (t1), the DCM for the conversion from body-frame to navigational-frame coordinates at time t1.
An increment of a variable is indicated with the symbol Δ. For example, Δ{right arrow over (x)} denotes the increment of the vector {right arrow over (x)} over a predefined time interval. An error in a variable is indicated with the symbol ô. For example, ô{right arrow over (x)} denotes the error in the vector {right arrow over (x)}. The symbol=indicates an approximate or substantially close equality.
Sensors and Orientation
In a two accelerometer arrangement, a first accelerometer is positioned to sense acceleration along the yb body axis that extends outward from the right side of the body. A second accelerometer is positioned to sense acceleration along the zb body axis that extends downward from the origin forming the yaw axis. A third accelerometer, not required for the computation of a roll variable, is positioned to sense acceleration along the xb or forward axis.
Roll Angle Computation
The accelerometer outputs are resolved from-body coordinates into navigational coordinate values in accordance with the following equation:
AN=CN b AB={T}{H}T {P}T {R}T AB  1a.
where Ab represents the acceleration vector in body coordinates, the bracketed H, P and R operators {H}T, {P}T{R}T individually represent the transpose of the positive rotation DCM transformation steps from body to navigational coordinates for the heading or yaw, about zb, pitch, about y and roll, about xb, of the vehicle or projectile fixed coordinate system, in that sequence, to obtain the acceleration vector AN as elements of vehicle acceleration in navigation coordinates with components along the fixed navigation or earth referenced East, X, North, Y and Up, Z axis.
DCM {T} represents a unitary matrix that transforms the body referenced acceleration data from a North, East, Down system into an East, North, Up frame and is defined as: { T } = Δ 0 1 0 1 0 0 0 0 - 1 1b.
Figure US06779752-20040824-M00001
The data elements of acceleration Ab, from the triad of accelerometers on the projectile, are integrated over a predetermined incremental time interval such as one second to obtain incremental changes in velocity in navigational coordinates in accordance with the following equation:
 ΔV N =∫C b N A b dt={T}{H} T {P} T {R} Y A b ΔT   2.
Concurrent with each calculation of the incremental change in velocity based on accelerometer data, GPS data is used to calculate an incremental change in velocity. The GPS data is already in navigational coordinates. The following equation is used:
ΔV GPS= V GPS2−V GPS1=ΔV N ={T}{H} T {P} T {R} T A b ΔT  3.
A double integration is performed on the body accelerometer data along with a body to navigation frame transformation to obtain the change in position based on transformed. accelerometer data from the body frame using the following equation:
ΔP N =∫∫C b N A b dtdτ={T}{H} T {P} T {R} T A b ΔT 2  4.
With each calculation of the incremental change in position based on accelerometer data, ΔPN, GPS data is used to calculate a substantially equal GPS incremental change in position, ΔPGPS The following equation is used:
ΔP GPS =P GPS2 −P GPS1 =ΔP N ={T}{H} T {P} T {R} T A b ΔT 2  5.
Group Equations:
The product of a DCM matrix and its transpose is equal to the identity matrix. Therefore
{P}T {P}={I}  6a.
{H}T {H}={I}  6b.
From equation 3, it is possible to relate change in velocity components or accelerations components from the GPS data to acceleration components from accelerometer data as follows:
ΔVGPS={T}{H}T {P} T {R} T A b ΔT=ΔV N  7a.
From equation 5, it is possible to relate change in position components or velocity components from the GPS data to velocity components from accelerometer data as follows:
ΔV GPS={T}{H}T {P}T {R} T A b ΔT 2 =ΔP N  7b.
If the pitch, heading and unitary transformation DCMs are grouped or multiplied to form a single DCM, {Q}, and the increment in time is chosen for simplicity to be 1second (however, it should be understood that any time increment can be used in the equations):
{Q}={P}{H}{T}  8a.
ΔT=1 Second and Δ2=1 Second squared=1  8b.
Substituting 1 for ΔT in equation 7a and 1 for ΔT2 in equation 7b and multiplying both sides of equations 7a and 7b by the transpose of the unitary, heading and pitch DCMs, in that order, provides the following equations:
{P}{H}{T}(ΔVGPS)={R}AB={Q}(ΔVGPS)  9a.
{P}{H}{T}(ΔPGPS)={R}AB={Q}(ΔPGPS)  9b.
Using CP to represent Cos, θ SP to represent Sin θ, CH to represent Cos φ, SH to represent Sin φ, CR to represent Cos φ and SR to represent Sin φ, then the six DCMs for the rotation conversions from body to navigation coordinates are: { P } = Δ CP 0 - SP 0 1 0 SP 0 CP { P } T = Δ CP 0 SP 0 1 0 - SP 0 CP 10 a . { H } = Δ CH SH 0 - SH CH 0 0 0 1 { H } = Δ CP - SH 0 SH CH 0 0 0 1 and 10 b . { R } = Δ 1 0 0 0 CR SR 0 - SR CR { P } = Δ 1 0 0 0 CR - SR 0 SR CR 10 c .
Figure US06779752-20040824-M00002
Where the body is a projectile fired from a gun, the pitch angle is the angle of the barrel at firing and the beading is the angle ψ that the barrel makes with true north at firing. Both are available from initialization from the system and are expected to be close to the normal trajectory with time, and therefore nominally known.
The elements of {Q} are known from 8a, 10a, and 10b and are believed to be slowly varying, so let {Q} be: { Q } = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 11.
Figure US06779752-20040824-M00003
Rewriting equations 9a and 9b and substituting {Q} into the result for {P} {H} {T} with ΔT=1 second and ΔT2=1 second provides;
{Q}(ΔV GPS)={R}A B  12a.
{Q}(ΔP GPS)={R}A B  12b.
Reversing the left and right sides:
{R}A B ={Q}(ΔVGPS)  13a.
{R}A B ={Q}(ΔP GPS)  13b.
Since the roll DCM is characterized in 10c and accelerometer data is a vector:
{ R } = 1 0 0 0 CR SR 0 - SR CR 10 d .
Figure US06779752-20040824-M00004
A b =a 1 {circumflex over (x)} b +a 2 ŷ b +a 3 {circumflex over (z)}b   14.
where {circumflex over (x)}b, ŷb and {circumflex over (z)}b are unit vectors along the body axis.
Equations 13a and 13b are rewritten as: 1 0 0 0 CR SR 0 - SR CR a 1 a 2 a 3 = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 ( Δ V GPS _ ) 15 a . 1 0 0 0 CR SR 0 - SR CR a 1 a 2 a 3 = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 ( Δ P GPS _ ) 15 b .
Figure US06779752-20040824-M00005
The incremental accelerometer and velocity data from the GPS is made available in fixed navigation coordinates forming two three-element vectors
{overscore (ΔV GPS)}=ΔV x {circumflex over (x)}+ΔV y ŷ+ΔV z {circumflex over (z)} and  16a.
{overscore (ΔV GPS)}=ΔP x {circumflex over (x)}+ΔV y ŷ+ΔV z {circumflex over (z)}a  16b.
where, {circumflex over (x)}, ŷ and {circumflex over (z)} are basic unit vectors of the East, North and Up coordinate frame system.
The matrix for {Q} in 15a and 15b are multiplied by the vectors of 16a and 16b as: 1 0 0 0 CR SR 0 - SR CR a 1 a 2 a 3 = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 Δ V x Δ V y Δ V z 17 a . 1 0 0 0 CR SR 0 - SR CR a 1 a 2 a 3 = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 Δ P x Δ P y Δ P z 17 b .
Figure US06779752-20040824-M00006
The left sides of 17a and 17b are multiplied out forming a 3×1 matrix on the left: [ a 2 CR + a 3 SR a 1 - a 2 SR + a 3 CR ] = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 Δ V x Δ V y Δ V z 18 a . [ a 2 CR + a 3 SR a 1 - a 2 SR + a 3 CR ] = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 32 q 33 Δ P x Δ P y Δ P z 18 b .
Figure US06779752-20040824-M00007
The first element a1 of the vector on the left hand side of equations 18a and 18b, i.e., has no roll angle component because it represents acceleration down the vehicle's longitudinal axis, therefore it is deleted leaving only the second and third row expressions. From Equations 18a and 18b: [ a 2 CR + a 3 SR 1 - a 2 SR + a 3 CR ] = [ q 21 q 22 q 23 q 31 q 32 q 33 ] Δ V x Δ V y Δ V z 19 a . [ a 2 CR + a 3 SR 1 - a 2 SR + a 3 CR ] = [ q 21 q 22 q 23 q 31 q 32 q 33 ] Δ P x Δ P y Δ P z 19 b .
Figure US06779752-20040824-M00008
The left side of 19a and 19b can be rewritten to form a 2×2 matrix times a 2×1 matrix as: [ a 2 CR + a 3 SR 1 - a 2 SR + a 3 CR ] = [ a 2 a 3 a 3 - a 2 ] [ CR CR ] = [ q 21 q 22 q 23 q 31 q 32 q 33 ] V x Δ V y Δ V z 20 a . [ a 2 CR + a 3 SR - a 2 SR + a 3 CR ] = [ a 2 a 3 a 3 - a 2 ] [ CR CR ] = [ q 21 q 22 q 23 q 31 q 32 q 33 ] Δ P x Δ P y Δ P z 20 b .
Figure US06779752-20040824-M00009
Combining 20a and 2Db obtains: [ a 2 a 3 a 3 - a 2 a 2 a 3 a 3 - a 2 ] CR SR = [ q 21 q 22 q 23 0 0 0 q 31 q 32 q 33 0 0 0 0 0 0 q 21 q 22 q 23 0 0 0 q 31 q 32 q 33 ] [ Δ V x Δ V y Δ V z Δ V x Δ V y Δ V z ] 20 c .
Figure US06779752-20040824-M00010
A calculation of the roll angle will use the following definitions: a 1 = [ a 2 a 3 a 3 - a 2 a 2 a 3 a 3 - a 2 ] 20 d .
Figure US06779752-20040824-M00011
is the accelerometer coefficient matrix. β 1 = [ q 21 q 22 q 23 0 0 0 q 31 q 32 q 33 0 0 0 0 0 0 q 21 q 22 q 23 0 0 0 q 31 q 32 q 33 ] 20 e .
Figure US06779752-20040824-M00012
is the pitch/heading coefficient matrix. w 1 _ = [ Δ V X Δ V Y Δ V Z Δ V X Δ V Y Δ V Z ] 20 f .
Figure US06779752-20040824-M00013
is the GPS information vector and x 1 _ = [ CR SR ] 20 g .
Figure US06779752-20040824-M00014
is the unknown roll quantity. Rewriting Equation 20c provides:
a1 {overscore (x)}11 {overscore (ω)}1  21.
The a1 matrix is a 4×2 matrix. {overscore (χ)}1 is a 2×1 vector. Solving Equation 21 for {overscore (χ)}1, recognizing that Equation 21 represents four equations in two unknowns (CR, SR), proceeds with multiplying both sides of Equation 21 by a′1 a1 to provide:
 a1 T a1 {overscore (χ)}1=a1 T β1 {overscore (ω)}1  22a.
Pre-multiplying both sides by the inverse of the product of the a1 T a1 provides:
{overscore (χ)}1 =[a 1 T a 1 ]−1 a 1 T β1 {overscore (ω)}1  22b.
Therefore, since 23 a . χ _ 1 = [ CR SR ] = [ χ ( 1 ) χ ( 2 ) ]
Figure US06779752-20040824-M00015
the roll angle is:
Roll (φ=tan−1 1 (2)/χ1 (1)=tan−1 (SR/CR)  23b
This procedure is followed for additional sample times by again solving the over-determined system as follows. For t=t2 there will be eight equations with two unknowns (cos R, sin R) and for t=tn there will be 4n equations with two unknowns (cos R, sin R).
The iterative solution is found by stacking the equations as follows (i.e., for t=t2): 24. [ a 1 a 2 ] - χ _ 2 = [ β 1 ω _ 1 β 2 ω _ 2 ]
Figure US06779752-20040824-M00016
where a1, β1 and {overscore (ω)}1 have been defined above. The new variables a2 β2 and {overscore (ω)}2 have the same structure as a1, β1 and {overscore (ω)}1 except that they represent the values at t=t2. Also, {overscore (χ)}2 represents the values of cos R, sin R utilizing the variable over two lata samples. The solution at t=t2 is therefore obtained as before and as follows: 25. [ a 1 T a 2 T ] [ a 1 a 2 ] χ _ 2 = [ a 1 T a 2 t ] [ β 1 ω _ 1 β 2 ω _ 2 ] 26. χ _ 2 = [ i = 1 2 ( a i T a i ) ] - 1 [ i = 1 2 a i T β i ω _ i ]
Figure US06779752-20040824-M00017
Similarly at t=tn for n data samples, 27. χ _ n = [ i = 1 n ( a i T a i ) ] - 1 [ i = 1 n a i T β i ω i ] 28. Roll n = tan - 1 ( χ n ( 2 ) χ n ( 1 ) ) .
Figure US06779752-20040824-M00018
For a generalized projectile or vehicle we also need data for the pitch and heading coefficient matrix. The heading and pitch (no gyro) might be approximated from the ground track (arctan Vn/Ve), and the pitch from the flight path angle (arctan of the vertical velocity or rate of change of altitude and the ground speed as determined from delta P North and delta P east). A rough heading may be available from a magnetic compass or a solid state magnetic compass available from Honeywell. If the winds aloft are known, they might be used to correct the heading and if the angle of attack were known, it might be used to correct the pitch angle.
FIG. 5 is a block diagram that schematically provides an overview of the process functions necessary for roll angle computation. GPS RECEIVER, block 500 is shown with its internal computer providing POSITION and VELOCITY data via POSITION sampler 502, and VELOCITY SAMPLER 504. Each sampler has a respective sampler delay 506 and 508. The outputs of the samplers are A POSITION and Δ VELOCITY and this data is coupled to a ROLL ESTIMATE (Iterative Solution) functional block 510. The ACCELEROMETERS block 512 represents the triax of accelerometers aligned with the BODY AXES described earlier. The component of acceleration ax is aligned with the longitudinal axis of the projectile as shown in Figure The component of acceleration ax changes very slowly during the flight from one second to the next. The component of acceleration ay is the cross track acceleration and the az is the component of acceleration along the up axis both being shown in FIG. 1. The PITCH HEADING COEFFICIENT MATRIX 514 is initialized with ay and az accelerometer data. Processing of the data uses present PITCH ESTIMATE and HEADING ESTIMATE for trigonometric values. The input ΔT will be shown to have the preferred value of one second. The PITCH HEADING COEFFICIENT MATRIX is used with the GPS A POSITION and Δ VELOCITY inputs by the ROLL ESTIMATE functional block 510 to provide a roll angle φ output to the FLIGHT CONTROL block 516 which includes block 26 in FIG. 1.
Smoothing
The smoothing process referred to by block 344 in FIG. 3a will now be explained in connection with a discussion of FIGS. 6, 7 a and 7 b. The invention projectile guidance system with accelerometers and a GPS receiver outputs a smoothed estimate of the past trajectory of the projectile from launch to its present position, throughout its flight, to the FLIGHT CONTROL block 26, shown on FIGS. 1 and 5, along with the attitude angles to permit the flight control function 26 to adjust the heading or ground track of the projectile to the known target location.
FIG. 6 provides an embodiment of a forward smoother. The embodiment shown uses Kalman filter. The Kalman filter of block 364, on FIG. 3b is such a filter in which there have been n measurements {y1, y2, y2 . . . , yn} at times t1 t2, . . . , tn.
A measurement at time tk might contain acceleration data from an instrument or a velocity or a piece of position data or a sample of velocity or position data from a GPS input or from accelerometer data as delta V data and these values are arrayed as values of the y vector as {y1, y2, y2, . . . , yn}. We want an estimate of the system state at each update.
The process is time indexed or sample indexed with GPS information at a one Hz sample rate. Between GPS samples, the system reprocesses all past samples and states using the measurement index counter or k counter to provide an index as it counts from 1 to n.
The process has the objective of going back in time to obtain an educated estimate of the system state vector at an earlier sample time tk. Measurement data, such as GPS position data, is indexed as it is acquired or received as samples 1 through k with the last sample received being measurements indexed as sample n.
FIG. 6 starts at block 600 with the initialization of the covariance matrix P(0)=P(t0) at t=t0 based on a knowledge of the initial state of the process at startup. Block 602 shows that the sample index counter, the k counter, is then set to one and block 604 tests to see if time t is greater than tn. If time is less than or equal to tn, the test advances to block 606 and increments the index counter by one.
Block 608 represents the step of propagating the system state vector or estimated state vector x from time tk−1 to time φk−1. The symbol φk−1 represents the system equation or transfer function. The transfer function φk−1 propagates the state vector of the system x from time k−1 to time k. The state vector expressed as a state matrix “x” is a column matrix that is “m” by one in dimension. The covariance matrix P is “m” by “m” in dimension.
The processes advances to block 610. In this step, the flow chart propagates the covariance matrix P from tk−1 to tk, using the equation P{overscore (k)}=φk−1 Pk−1 φk−1 T Qk−1. In this equation, the term Pk is the error covariance associated with the filter estimate of the state vector x{overscore (k)}. The transfer function φk−1 and its transpose φk−1 T are introduced above. The term Qk−1 is the covariance matrix of the process noise.
In block 612, the process computes the Kalman filter gain for time t=tk. The symbol Gk represents the Kalman gain. The term Hk is the measurement or observation matrix at time t=tk, and Hk T represents the transpose of the measurement matrix at time t=tk. The measurement matrix will typically be formed from elements such as Vx, Vy. The y vector or measurement vector is formed from the product of the H matrix and the state vector x the product being added to the measurement noise matrix.
Within the brackets of the expression in block 612, the error covariance matrix P{overscore (k)} is multiplied by the transpose of the measurement matrix Hk T. The product of the two is then multiplied by the measurement matrix Hk. The result of the product is added to Rk, the covariance matrix of the measurement noise vector.
The Rk matrix is obtained from information that is gathered by the systems engineers through empirical testing. The systems engineers determine what noise is associated with each sensor by collecting historical noise data on each measurement variable. The Hk matrix is given and is hardware and instrument dependent. The Kalman gain is determined and then used to update the estimate of the state vectors in block 614. As each measurement is taken, it is itself a function of a combination of the states. For example, the velocity of a projectile might be the result of x and y velocity components. The result is a linear combination of the individual measurements.
The process advances to block 614 and the system state estimate vector is updated for time tk using the equation: {circumflex over (x)}k={circumflex over (x)}{overscore (k)}+Gk [yk−Hk {circumflex over (x)}{overscore (k)}]. The term Hk multiplies the term {circumflex over (x)}{overscore (K)}. The result is subtracted from Yk. The result is an observable difference that is multiplied by the Kalman gain and then added to the previously estimated state vector {circumflex over (x)}{overscore (K)}.
The minus sign in the superscript of {circumflex over (x)}{overscore (K)} implies that it represents the state a little before the kth update. The sample index “k” can range in value from 1 to n where n is the most recent update index in time. A state variable without a superscript implies that the state variable value is a value that exists just after an update. The symbol {circumflex over (x)}{overscore (K)} represents the kth estimate of the state vector x. When the yk measurement is made, the kth update is performed for the yk measurement. The measurement index “k” is a running index.
After updating the state vector at time t=tk by evaluating the equation in block 614, the process proceeds to the equation in block 616:
P k =[I−G k H k ]P{overscore (k)},
which is used to update the covariance matrix Pk The matrix 1 is an identity matrix. All of its elements are zero except the main diagonal elements which are nes. The dimension of the identity matrix is matched to the product of Gk and Hk matrices. All of the values necessary for the computation of the covariance matrix are available from previous steps.
After the computation of the Pk matrix, the process leaves block 616 and transfers back to decision block 604 to once again test to see if t>tn. As time reaches tn, all of the measurements have been processed. No additional measurements are to be made. A “yes” result transfers the process to the Scenario Complete block 618 and the mission is completed. If the flight had lasted one hundred seconds and the GPS provided position measurements at one per second, there would have been 100 GPS samples and the sample index k would have been incremented from 1 to 100. The index “k” can not exceed 100.
FIGS. 7a and 7 b form a fixed interval smoother, FIG. 7a providing a forward pass and FIG. 7b providing a backward pass. FIG. 7a can be seen to be identical in function to that of FIG. 6 with the exception of blocks 700. The process exits block and advances to block 702 also found at the top of FIG. 7b. The backward sweep begins with block 704 as the process sets the sample index counter, i.e., the k counter to current index value of n. The object of the backward sweep process of FIG. 7b is to compute the smoother estimate xs (k)={circumflex over (x)}(k|n) and the smoother error covariance Ps (k)=P(k|n), using all n measurements as the measurement index counter “k” is decremented k=n, n−1, n−2, . . . , 1. A subscript “s” in the expression xs (k) and in the expression Ps(k) indicates a smoothed variable.
The process advances to block 706 to compute smoother gain:
A(k)=P(kk T P −1 (k+1|k)
The vertical bar followed by a “k” in a term such as (k|k) means that the matrix will be evaluated for all measurements up to and including the kth measurement. The backward sweep begins only after the conclusion of a forward sweep. All k measurements are available at the conclusion of the forward sweep. All k data points form a fixed interval, and all n measurements from tk back to t1 are used during the backward sweep.
The covariance matrix P(k|k) is multiplied with the transpose of the transfer function φk at time t=k.
The rightmost term in block 706 is the inverse of the covariance matrix P(k+1|k) at time tk+1 using all k measurements. The vertical bar followed by “k” shows that all of the data for measurements through k is to be used.
The process then advances to block 708. The object of the equation in block 708 is to compute a smoothed state vector {circumflex over (x)}(k|n) using all n measurements. The equation in block 708 is:
{circumflex over (x)}(k|n)={circumflex over (x)}(k|k)+A(k)[{circumflex over (x)}(k+1|n)−{circumflex over (x)}(k+1|k)]
The gain matrix A(k is available from block 706. The first term after the equal sign is the kth state vector estimate using measurement data through measurement k. The first term inside of the bracket, the term {circumflex over (x)}(k+1|n) represents the estimate of the state vector at time k+1 using data for all measurements through measurement n. The second term inside of the bracket {circumflex over (x)}(k+1|k) is an estimate of the state vector at time k+1 using all measurements up to time tk. The difference is calculated as the second term is subtracted from the first. The result is multiplied by the gain matrix, the product is added to {circumflex over (x)}(k|k).
The process then advances to block 710 to compute a smoothed covariance matrix from the equation:
P(k|n)=P(k|k)+A(k)[P(k+1|n)−P(k+1|k)]A T (k)
The first covariance term after the equal sign P(k|k) uses all data through the kth update. The first covariance term in the bracket P(k+1|n) uses all of the data from measurements through measurement n. The second covariance term in the bracket P(k+1|k) uses only data up though the kth update. A covariance difference is calculated from the covariance terms within the brackets. The covariance difference term is then multiplied by the gain matrix and the result is added to P(k|k).
After the smoothed covariance estimate is calculated, the process advances to block 712 and decrements the measurement index counter from k to k−1. The process then advances to decision block 714 and a test is made to determine if the measurement index matrix k is greater than one. Looping or cycling continues with each “no” decision followed by a cycle back to block 706 until k=1. When k=1, the test at block 714 results in a “yes” decision and the process advances to block 716, the Backward Sweep Complete block. Block 716 signals the conclusion of the program as the projectile nears its target.
Those skilled in the art will appreciate that various adaptations and modifications of the preferred embodiments can be configured without departing from the scope and spirit of the invention. Therefore, it is to be understood that the invention may be practiced other than as specifically described herein within the scope of the appended claims.

Claims (36)

What is claimed is:
1. A projectile guidance system with accelerometers and a GPS receiver comprising:
a projectile having a triax of accelerometers mounted in the projectile and providing roll, pitch and azimuth axis acceleration data;
a GPS antenna and receiver means mounted in the projectile for providing and updating present position data; and
a computer and memory mounted in the projectile and executing a guidance program;
wherein the guidance program is responsive to the roll, pitch and azimuth axis acceleration data and to the sampled present position data for calculating and outputing time indexed roll, pitch and azimuth angles, time indexed present position and velocity to a flight control system for guiding the projectile to a predetermined target location;
wherein the GPS antenna and receiver means comprises a GPS jamming detector configured to detect the presence of GPS jamming in the present position data; and
wherein the GPS antenna and receiver means further comprises anti-jamming means.
2. The projectile guidance system of claim 1 wherein the GPS antenna and receiver means comprises a plurality of antennas, each antenna oriented to receive GPS signals from a unique direction.
3. The projectile guidance system of claim 1 wherein said anti-jamming means is configured to cause the projectile to engage in a periodic motion.
4. The projectile guidance system of claim 3 wherein the guidance program is configured to cause trajectory corrections to be made while the projectile is engaged in periodic motion by waiting for an orientation of a control surface to correspond with a direction in which it is desirable to steer the projectile.
5. The projectile guidance system of claim 3 wherein the guidance program is further configured to cause the periodic motion of the projectile to terminate and to therafter cause trajectory corrections to be made while the periodic motion of the projectile has terminated.
6. The projectile guidance system of claim 5 wherein the guidance program is further configured to determine the roll orientation of the projectile using a signal produced by a roll gyro.
7. The projectile guidance system of claim 5 wherein the guidance program is further configured to determine the roll orientation of the projectile using a roll position of a GPS satellites.
8. The projectile guidance system of claim 5 wherein the guidance program is further configured to determine the roll orientation of the projectile using a GPS attitude determination with a plurality of antennas.
9. The projectile guidance system of claim 5 wherein the guidance program is further configured to determine the roll orientation of the projectile using a magnetic turns counter.
10. The projectile guidance system of claim 1 wherein said anti-jamming means is configured to selectively and periodically avoid GPS signals that exhibit jamming.
11. The projectile guidance system of claim 1 wherein said anti-jamming means is configured to cause the projectile to maintain an orientation of the GPS antenna and receiver means so as to permit one or more antenna to substantially continuously receive an unjammed GPS signal.
12. The projectile guidance system of claim 11 wherein, in the event no unjammed GPS signal may be substantially continuously received, said anti-jamming means is further configured to cause the projectile to engage in a periodic motion and to selectively and periodically avoid GPS signals that exhibit jamming.
13. The projectile guidance system of claim 1 wherein the GPS antenna and receiver means is configured to convert a GPS signal from an RF signal to a digital GPS signal substantially immediately after reception.
14. The projectile guidance system of claim 13 wherein the GPS antenna and receiver means is further configured send said digital GPS signal through a digitally implemented automatic gain control circuit.
15. The projectile guidance system of claim 1 wherein the guidance program is further characterized to calculate an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle and the target destination.
16. The projectile guidance system of claim 1 wherein the guidance program is further characterized to calculate an estimated projectile trajectory based on data including the launch site present position, initial pitch azimuth angle, the target destination and data from a turns counter.
17. The projectile guidance system of claim 1 wherein the guidance program is further characterized to calculate an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle, the target destination, data from a turns counter, and a forward sweep recursive filter responsive to previously stored time indexed data for calculating and smoothing an estimated projectile trajectory, and outputting the smoothed time indexed trajectory data to the flight control system for use in guiding the projectile to the predetermined target location after each present position data update.
18. The projectile guidance system of claim 1 wherein the guidance program is further characterized to calculate an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, and azimuth angle, the target destination, data from a turns counter, a forward sweep recursive filter and a backward sweep recursive filter, each respective filter being responsive to previously stored time indexed data for calculating and smoothing an estimated projectile trajectory and outputing the smoothed time indexed trajectory data to the flight control system for use in guiding the projectile to the predetermined target location.
19. The projectile guidance system of claim 1 wherein the guidance program is further characterized to calculate an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle, the target destination, data from a turns counter, a forward Kalman sweep recursive filter and a backward sweep recursive filter, each respective filter being responsive to previously stored time indexed data for calculating and outputing a smoothed estimated projectile trajectory, and iterating the data comprising the smoothed time indexed trajectory data and outputing the smoothed time indexed trajectory data to the flight control system for use in guiding the projectile to the target location.
20. A projectile guidance system without gyros comprising:
a projectile or vehicle in flight after launch, the projectile having an orthogonal body coordinate system with
a longitudinal or x-axis for roll measurement,
a y-axis for pitch measurement, and a
a z-axis for yaw measurement,
the projectile having at least a triax of accelerometers comprising an x accelerometer for providing x-axis acceleration data measured along the x-axis, a accelerometer for providing yaxis acceleration data measured along the y-axis and a z-accelerometer for providing z-axis acceleration data measured along the z-axis,
a GPS antenna and receiver means for providing onboard GPS position and GPS velocity data in earth referenced navigational coordinates,
a computer and memory and program means for storing and accessing time indexed GPS position and GPS velocity data and for transforming
the x, y and z axis acceleration data from body to navigation coordinates, the acceleration data being arrayed and having time indexes common with the OPS position and velocity data,
the program means being responsive to corresponding time indexed acceleration data and to GPS velocity and position data for calculating and outputing an estimated projectile roll, pitch and yaw angle with respect to local level for each time index iteration of present position, velocity and acceleration data to a flight control system for guiding the projectile to a predetermined target location;
wherein the GPS antenna and receiver means comprises a GPS jamming detector configured to detect the presence of GPS jamming in the present position data; and
wherein the GPS antenna and receiver means further comprises anti-jamming means.
21. The projectile guidance system of claim 20 wherein the GPS antenna and receiver means comprises a plurality of antennas, each antenna oriented to receive GPS signals from a unique direction.
22. The projectile guidance system of claim 20 wherein said anti-jamming means is configured to cause the projectile to engage in a periodic motion.
23. The projectile guidance system of claim 22 wherein the guidance program is configured to cause trajectory corrections to be made while the projectile is engaged in periodic motion by waiting for an orientation of a control surface to correspond with a direction in which it is desirable to steer the projectile.
24. The projectile guidance system of claim 22 wherein the guidance program is further configured to cause the periodic motion of the projectile to terminate and to thereafter cause trajectory corrections to be made while the periodic motion of the projectile is terminated.
25. The projectile guidance system of claim 20 wherein said anti-jamming means is configured to selectively and periodically avoid GPS signals that exhibit jamming.
26. The projectile guidance system of claim 20 wherein said anti jamming means is configured to cause the projectile to maintain an orientation of the GPS antenna and receiver means so as to permit one or more antenna to substantially continuously receive an unjammed GPS signal.
27. The projectile guidance system of claims 26 wherein, in the event no unjammed GPS signal may be substantially continuously received, said anti-jamming means is further configured to cause the projectile to engage in a periodic motion and to selectively and periodically avoid GPS signals that exhibit jamming.
28. The projectile guidance system of claim 20 wherein the GPS antenna and receiver means is configured to convert a GPS signal from an RF signal to a digital GPS signal substantially immediately after reception.
29. The projectile guidance system of claim 28 wherein the GPS antenna and receiver means is further configured send said digital GPS signal through a digitally implemented automatic gain control circuit.
30. A process for the guidance of a vehicle or projectile, the vehicle having been launched and having an orthogonal coordinate system with a longitudinal or x-axis for roll measurement, a y-axis for pitch measurement, and a z-axis for yaw measurement, a triax of accelerometers outputing x, y and z axis acceleration, and a GPS antenna and receiver means for providing GPS position and GPS velocity data in earth referenced navigational coordinates, the process comprising the steps of:
receiving, indexing and storing GPS position and velocity data with concurrent x, y and z axis acceleration data;
calculate a trajectory for the set;
converting the x, y and z axis acceleration data to a local level navigational reference system;
solving a set of time indexed state equations to update the system's estimated state;
computing a time indexed pitch, roll and yaw angle in locally level coordinates;
outputing the time indexed pitch, roll and yaw angle in locally level coordinates with a corresponding time indexed present position;
guiding the projectile to a destination using the outputted time indexed pitch, roll, yaw angle and time indexed present position data;
the detecting presence of GPS jamming in the present position data; and
counteracting the GPS jamming in the present position data.
31. The process of claim 30 wherein, before the step of receiving, indexing and storing GPS position and velocity data with concurrent x, y and z axis acceleration data, performing the steps of:
estimating and providing a set of initial conditions for insertion into a set of state equations and;
calculating a trajectory for the vehicle as a function of the set of state equations, and the estimated initial conditions.
32. The process of claim 30 wherein, after the step of outputing the time indexed pitch, roll and yaw angle in locally level coordinates with a corresponding time indexed present position, performing the step of:
calculating an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle and the target destination.
33. The process of claim 30 wherein, after the step of outputing the time indexed pitch, roll and yaw angle in locally level coordinates with a corresponding time indexed present position, performing the step of:
calculating an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle and the target destination and data from a turns counter.
34. The process of claim 30 wherein, after the step of outputing the time indexed pitch, roll and yaw angle in locally level coordinates with a corresponding time indexed present position, performing the steps of:
calculating an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle and the target destination and data from a turns counter;
using a forward sweep recursive filter responsive to previously stored time indexed data for calculating and smoothing an estimated projectile trajectory; and
guiding the projectile to the predetermined target location using the smoothed time indexed trajectory data.
35. The process of claim 30 wherein, after the step of outputing the time indexed pitch, roll and yaw angle in locally level coordinates with a corresponding time indexed present position, performing the steps of:
calculating an estimated projectile trajectory based on data including the launch site present position, initial pitch angle, azimuth angle and the target destination and data from a turns counter; and
using a forward sweep recursive filter and a backward sweep recursive filter, responsive to previously stored time indexed data for calculating and smoothing an estimated projectile trajectory.
36. A projectile guidance system without gyros comprising:
a projectile or vehicle in flight after launch, the projectile having an orthogonal body coordinate system with
a longitudinal or x-axis for roll measurement,
a y-axis for pitch measurement, and a
a z-axis for yaw measurement,
the projectile having at least a triax of accelerometers comprising an x accelerometer for providing x-axis acceleration data measured along the x-axis, a y-accelerometer for providing y-axis acceleration data measured along the y-axis and a z-accelerometer for providing z-axis acceleration data measured along the z-axis,
a GPS antenna and receiver means for providing onboard GPS position and GPS velocity data in earth referenced navigational coordinates,
a computer and memory and program means for storing and accessing time indexed OPS position and GPS velocity data and for transforming
the x, y and z axis acceleration data from body to navigation coordinates, the acceleration data being arrayed and having time indexes common with the GPS position and velocity data,
the program means being responsive to corresponding time indexed acceleration data and to GPS velocity and position data for calculating and outputing an estimated projectile roll, pitch and yaw angle with respect to local level for each time index iteration of present position, velocity and acceleration data to a flight control system for guiding the projectile to a predetermined target location;
wherein the GPS antenna and receiver means comprises a GPS jamming detector configured to detect the presence of GPS jamming in the present position data; and
wherein the GPS antenna and receiver means further comprises anti-jamming means.
US10/396,639 2003-03-25 2003-03-25 Projectile guidance with accelerometers and a GPS receiver Expired - Fee Related US6779752B1 (en)

Priority Applications (6)

Application Number Priority Date Filing Date Title
US10/396,639 US6779752B1 (en) 2003-03-25 2003-03-25 Projectile guidance with accelerometers and a GPS receiver
JP2004571469A JP2006514258A (en) 2003-03-25 2003-11-12 Projectile guidance using accelerometers and GPS receivers
EP03783294A EP1606571A1 (en) 2003-03-25 2003-11-12 Projectile guidance with accelerometers and a gps receiver
CA002519935A CA2519935A1 (en) 2003-03-25 2003-11-12 Projectile guidance with accelerometers and a gps receiver
PCT/US2003/035849 WO2004097329A1 (en) 2003-03-25 2003-11-12 Projectile guidance with accelerometers and a gps receiver
AU2003290711A AU2003290711A1 (en) 2003-03-25 2003-11-12 Projectile guidance with accelerometers and a gps receiver

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US10/396,639 US6779752B1 (en) 2003-03-25 2003-03-25 Projectile guidance with accelerometers and a GPS receiver

Publications (1)

Publication Number Publication Date
US6779752B1 true US6779752B1 (en) 2004-08-24

Family

ID=32869145

Family Applications (1)

Application Number Title Priority Date Filing Date
US10/396,639 Expired - Fee Related US6779752B1 (en) 2003-03-25 2003-03-25 Projectile guidance with accelerometers and a GPS receiver

Country Status (6)

Country Link
US (1) US6779752B1 (en)
EP (1) EP1606571A1 (en)
JP (1) JP2006514258A (en)
AU (1) AU2003290711A1 (en)
CA (1) CA2519935A1 (en)
WO (1) WO2004097329A1 (en)

Cited By (41)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050031125A1 (en) * 2003-08-08 2005-02-10 Arthur Acampora Global-positioning-system data integrator and distribution system
US20060046636A1 (en) * 2002-11-22 2006-03-02 Pascal Chevalier Method for verifying anti-scrambling efficiency of a communication system
US7275691B1 (en) * 2003-11-25 2007-10-02 Curtis Wright Artillery fire control system
US20070282529A1 (en) * 2006-05-31 2007-12-06 Honeywell International Inc. Rapid self-alignment of a strapdown inertial system through real-time reprocessing
US20080003899A1 (en) * 2004-02-11 2008-01-03 Econtrols, Inc. Watercraft speed control device
US20080003900A1 (en) * 2004-02-11 2008-01-03 Econtrols, Inc. Watercraft speed control device
US20080001022A1 (en) * 2005-10-05 2008-01-03 Raytheon Company Precision targeting
US20080009206A1 (en) * 2004-02-11 2008-01-10 Econtrols, Inc. Watercraft speed control device
US20080009205A1 (en) * 2004-02-11 2008-01-10 Econtrols, Inc. Watercraft speed control device
US20080035785A1 (en) * 2006-02-16 2008-02-14 Lfk-Lenkflugkoerpersysteme Gmbh Unmanned missile and method for determining the position of an unmanned missile which may be uncoupled from an aircraft
US20080085642A1 (en) * 2006-10-04 2008-04-10 Econtrols, Inc. Method for engaging a watercraft speed control system
US20080102774A1 (en) * 2006-10-27 2008-05-01 Fratti Roger A Automatic gain control for enhanced bit error rate performance
US20080113568A1 (en) * 2004-02-11 2008-05-15 Econtrols, Inc. Watercraft speed control device
US20080243321A1 (en) * 2005-02-11 2008-10-02 Econtrols, Inc. Event sensor
US20090209152A1 (en) * 2005-02-11 2009-08-20 Econtrols, Inc. Watercraft speed control device
US20090209153A1 (en) * 2004-02-11 2009-08-20 Econtrols, Inc. Watercraft speed control device
US20100044495A1 (en) * 2006-10-24 2010-02-25 Rafael Advanced Defense Systems Ltd. Airborne guided shell
US20100052981A1 (en) * 2008-08-29 2010-03-04 Alexander Steven B Systems and methods for determining a rotational position of an object
US20100289687A1 (en) * 2009-05-15 2010-11-18 Mayflower Communications Company, Inc. Antijam protected GPS-based measurement of roll rate and roll angle of spinning platforms
US20110022297A1 (en) * 1997-02-25 2011-01-27 George W. Hindman Apparatus and method for a mobile navigation computer
US8076622B1 (en) * 2009-08-31 2011-12-13 Rockwell Collins, Inc. Low profile, conformal global positioning system array for artillery
US8212195B2 (en) 2009-01-23 2012-07-03 Raytheon Company Projectile with inertial measurement unit failure detection
US8237096B1 (en) 2010-08-19 2012-08-07 Interstate Electronics Corporation, A Subsidiary Of L-3 Communications Corporation Mortar round glide kit
WO2013043097A1 (en) * 2011-09-20 2013-03-28 Bae Systems Bofors Ab Method and gnc system for determination of roll angle
US8475221B1 (en) 2004-02-11 2013-07-02 Econtrols, Inc. Watercraft speed control device
US8521348B1 (en) 2004-02-11 2013-08-27 Econtrols, Inc. Watercraft speed control device
US8718587B2 (en) * 2012-04-18 2014-05-06 Qualcomm Incorporated Reconfigurable LNA for increased jammer rejection
US9052717B1 (en) 2004-02-11 2015-06-09 Enovation Controls, Llc Watercraft speed control device
US9115968B1 (en) * 2014-02-12 2015-08-25 The United States Of America As Represented By The Secretary Of The Army Course self-correcting projectile
US20150263434A1 (en) 2013-03-15 2015-09-17 SeeScan, Inc. Dual antenna systems with variable polarization
US9156372B1 (en) 2011-04-26 2015-10-13 Enovation Controls, Llc Multinodal ballast and trim control system and method
US9207675B1 (en) 2005-02-11 2015-12-08 Enovation Controls, Llc Event sensor
US9366514B1 (en) * 2014-02-25 2016-06-14 Lockheed Martin Corporation System, method and computer program product for providing for a course vector change of a multiple propulsion rocket propelled grenade
US9645251B1 (en) * 2014-03-26 2017-05-09 Exelis Inc. Estimation of roll and roll rate of a spinning body based on a signal received from a remote transmitter
CN107152895A (en) * 2017-06-21 2017-09-12 北京瑞极通达科技有限公司 A kind of conformal radar surveys height/global location set composite
CN107631666A (en) * 2017-09-29 2018-01-26 西安交通大学 A kind of body roll angle detecting system and method based on earth magnetism and sun optic angle
US9983315B1 (en) * 2015-05-29 2018-05-29 Interstate Electronics Corporation Satellite navigation receiver for a rapidly rotating object with improved resistance to jamming
US10608348B2 (en) 2012-03-31 2020-03-31 SeeScan, Inc. Dual antenna systems with variable polarization
US10705221B2 (en) * 2016-06-08 2020-07-07 The Boeing Company On-board backup and anti-spoofing GPS system
US11543539B2 (en) 2018-09-21 2023-01-03 Subaru Corporation Aircraft flight control apparatus, aircraft flight controlling method, and non-transitory storage medium
CN115659103A (en) * 2022-12-27 2023-01-31 北京航天众信科技有限公司 Method, device, medium and equipment for calculating roll angle of rotating target

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6883747B2 (en) 2003-03-28 2005-04-26 Northrop Grumman Corporation Projectile guidance with accelerometers and a GPS receiver
JP2009103488A (en) * 2007-10-22 2009-05-14 Ihi Aerospace Co Ltd Positioning device of missile
JP5501726B2 (en) * 2009-10-16 2014-05-28 三菱重工業株式会社 Vehicle suspension device and vehicle equipped with the same
KR20130035483A (en) * 2011-09-30 2013-04-09 삼성전자주식회사 Apparatus and method for perceiving heading change in mobile terminal
JP5565644B1 (en) * 2013-02-15 2014-08-06 防衛省技術研究本部長 Measuring system and measuring method for measuring output frequency error of oscillator built in GPS receiver
KR101750503B1 (en) * 2016-09-09 2017-06-23 엘아이지넥스원 주식회사 Apparatus for processing navigation signal with function for eliminating GPS jamming signal
CN109798902B (en) * 2019-03-11 2020-09-22 北京星际荣耀空间科技有限公司 Iterative guidance method suitable for carrier rocket in-orbit correction

Citations (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5260709A (en) * 1991-12-19 1993-11-09 Hughes Aircraft Company Autonomous precision weapon delivery using synthetic array radar
US5507452A (en) * 1994-08-24 1996-04-16 Loral Corp. Precision guidance system for aircraft launched bombs
US5554994A (en) * 1995-06-05 1996-09-10 Hughes Missile Systems Company Self-surveying relative GPS (global positioning system) weapon guidance system
US5657947A (en) * 1994-08-24 1997-08-19 Loral Corp. Precision guidance system for aircraft launched bombs
US6003809A (en) * 1997-02-25 1999-12-21 Honigsbaum; Richard F. Process and apparatus for discouraging countermeasures against a weapon transport device
US6037899A (en) * 1997-05-05 2000-03-14 Rheinmetall W&M Gmbh Method for vectoring active or combat projectiles over a defined operative range using a GPS-supported pilot projectile
US6157875A (en) * 1998-07-17 2000-12-05 The United States Of America As Represented By The Secretary Of The Navy Image guided weapon system and method
US6163021A (en) * 1998-12-15 2000-12-19 Rockwell Collins, Inc. Navigation system for spinning projectiles
US6237496B1 (en) * 1997-02-26 2001-05-29 Northrop Grumman Corporation GPS guided munition
US6254031B1 (en) * 1994-08-24 2001-07-03 Lockhead Martin Corporation Precision guidance system for aircraft launched bombs
US6317688B1 (en) * 2000-01-31 2001-11-13 Rockwell Collins Method and apparatus for achieving sole means navigation from global navigation satelite systems
US6573486B1 (en) * 2002-02-22 2003-06-03 Northrop Grumman Corporation Projectile guidance with accelerometers and a GPS receiver

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5432520A (en) * 1993-10-18 1995-07-11 Hughes Aircraft Company SAR/GPS inertial method of range measurement
DE19500993A1 (en) * 1995-01-14 1996-07-18 Contraves Gmbh Establishing roll attitude of rolling flying object, e.g rocket or other projectile
US6449559B2 (en) * 1998-11-20 2002-09-10 American Gnc Corporation Fully-coupled positioning process and system thereof
US20020017977A1 (en) * 2000-08-04 2002-02-14 Wall Mark Emanuel Method and apparatus for licensing and controlling access, use, and viability of product utilizing geographic position

Patent Citations (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5260709A (en) * 1991-12-19 1993-11-09 Hughes Aircraft Company Autonomous precision weapon delivery using synthetic array radar
US5507452A (en) * 1994-08-24 1996-04-16 Loral Corp. Precision guidance system for aircraft launched bombs
US5657947A (en) * 1994-08-24 1997-08-19 Loral Corp. Precision guidance system for aircraft launched bombs
US6254031B1 (en) * 1994-08-24 2001-07-03 Lockhead Martin Corporation Precision guidance system for aircraft launched bombs
US5554994A (en) * 1995-06-05 1996-09-10 Hughes Missile Systems Company Self-surveying relative GPS (global positioning system) weapon guidance system
US6003809A (en) * 1997-02-25 1999-12-21 Honigsbaum; Richard F. Process and apparatus for discouraging countermeasures against a weapon transport device
US6237496B1 (en) * 1997-02-26 2001-05-29 Northrop Grumman Corporation GPS guided munition
US6037899A (en) * 1997-05-05 2000-03-14 Rheinmetall W&M Gmbh Method for vectoring active or combat projectiles over a defined operative range using a GPS-supported pilot projectile
US6157875A (en) * 1998-07-17 2000-12-05 The United States Of America As Represented By The Secretary Of The Navy Image guided weapon system and method
US6163021A (en) * 1998-12-15 2000-12-19 Rockwell Collins, Inc. Navigation system for spinning projectiles
US6317688B1 (en) * 2000-01-31 2001-11-13 Rockwell Collins Method and apparatus for achieving sole means navigation from global navigation satelite systems
US6573486B1 (en) * 2002-02-22 2003-06-03 Northrop Grumman Corporation Projectile guidance with accelerometers and a GPS receiver

Cited By (75)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110022297A1 (en) * 1997-02-25 2011-01-27 George W. Hindman Apparatus and method for a mobile navigation computer
US7346310B2 (en) * 2002-11-22 2008-03-18 Thales Method for verifying anti-scrambling efficiency of a communication system
US20060046636A1 (en) * 2002-11-22 2006-03-02 Pascal Chevalier Method for verifying anti-scrambling efficiency of a communication system
US20050029395A1 (en) * 2003-08-08 2005-02-10 Anderson Donald B. Hot-start navigation information distribution system
US7080804B2 (en) * 2003-08-08 2006-07-25 Lockheed Martin Corporation Hot-start navigation information distribution system
US20050031125A1 (en) * 2003-08-08 2005-02-10 Arthur Acampora Global-positioning-system data integrator and distribution system
US7275691B1 (en) * 2003-11-25 2007-10-02 Curtis Wright Artillery fire control system
US7485021B2 (en) 2004-02-11 2009-02-03 Econtrols, Inc. Watercraft speed control device
US20090209153A1 (en) * 2004-02-11 2009-08-20 Econtrols, Inc. Watercraft speed control device
US20080009206A1 (en) * 2004-02-11 2008-01-10 Econtrols, Inc. Watercraft speed control device
US20080009205A1 (en) * 2004-02-11 2008-01-10 Econtrols, Inc. Watercraft speed control device
US8475221B1 (en) 2004-02-11 2013-07-02 Econtrols, Inc. Watercraft speed control device
US20080003900A1 (en) * 2004-02-11 2008-01-03 Econtrols, Inc. Watercraft speed control device
US8521348B1 (en) 2004-02-11 2013-08-27 Econtrols, Inc. Watercraft speed control device
US8145372B2 (en) 2004-02-11 2012-03-27 Econtrols, Inc. Watercraft speed control device
US20080113568A1 (en) * 2004-02-11 2008-05-15 Econtrols, Inc. Watercraft speed control device
US9052717B1 (en) 2004-02-11 2015-06-09 Enovation Controls, Llc Watercraft speed control device
US7465203B2 (en) 2004-02-11 2008-12-16 Econtrols, Inc. Watercraft speed control device
US20080003899A1 (en) * 2004-02-11 2008-01-03 Econtrols, Inc. Watercraft speed control device
US7491104B2 (en) 2004-02-11 2009-02-17 Econtrols, Inc. Watercraft speed control device
US7494393B2 (en) 2004-02-11 2009-02-24 Econtrols, Inc. Watercraft speed control device
US7494394B2 (en) 2004-02-11 2009-02-24 Econtrols, Inc. Watercraft speed control device
US20090209152A1 (en) * 2005-02-11 2009-08-20 Econtrols, Inc. Watercraft speed control device
US9068838B1 (en) 2005-02-11 2015-06-30 Enovation Controls, Llc Event sensor
US9207675B1 (en) 2005-02-11 2015-12-08 Enovation Controls, Llc Event sensor
US9098083B1 (en) 2005-02-11 2015-08-04 Enovation Controls, Llc Event sensor
US8983768B1 (en) 2005-02-11 2015-03-17 Enovation Controls, Llc Event sensor
US9092033B1 (en) 2005-02-11 2015-07-28 Enovation Controls, Llc Event sensor
US7877174B2 (en) 2005-02-11 2011-01-25 Econtrols, Inc. Watercraft speed control device
US20080243321A1 (en) * 2005-02-11 2008-10-02 Econtrols, Inc. Event sensor
US7728264B2 (en) * 2005-10-05 2010-06-01 Raytheon Company Precision targeting
US20080001022A1 (en) * 2005-10-05 2008-01-03 Raytheon Company Precision targeting
US7960675B2 (en) * 2006-02-16 2011-06-14 Lfk-Lenkflugkoerpersysteme Gmbh Unmanned missile and method for determining the position of an unmanned missile which may be uncoupled from an aircraft
US20080035785A1 (en) * 2006-02-16 2008-02-14 Lfk-Lenkflugkoerpersysteme Gmbh Unmanned missile and method for determining the position of an unmanned missile which may be uncoupled from an aircraft
US7739045B2 (en) * 2006-05-31 2010-06-15 Honeywell International Inc. Rapid self-alignment of a strapdown inertial system through real-time reprocessing
US20070282529A1 (en) * 2006-05-31 2007-12-06 Honeywell International Inc. Rapid self-alignment of a strapdown inertial system through real-time reprocessing
US20080085642A1 (en) * 2006-10-04 2008-04-10 Econtrols, Inc. Method for engaging a watercraft speed control system
US8278611B2 (en) * 2006-10-24 2012-10-02 Rafael Advanced Defense Systems Ltd. Airborne guided shell
US20100044495A1 (en) * 2006-10-24 2010-02-25 Rafael Advanced Defense Systems Ltd. Airborne guided shell
US8175562B2 (en) * 2006-10-27 2012-05-08 Agere Systems Inc. Automatic gain control for enhanced bit error rate performance
US20080102774A1 (en) * 2006-10-27 2008-05-01 Fratti Roger A Automatic gain control for enhanced bit error rate performance
US8711035B1 (en) 2008-08-29 2014-04-29 Interstate Electronics Corporation Systems and methods for tracking power modulation
US11287534B1 (en) 2008-08-29 2022-03-29 Interstate Electronics Corporation Systems and methods for tracking power modulation
US8199052B1 (en) 2008-08-29 2012-06-12 Interstate Electronics Corporation Systems and methods for determining a rotational position of an object
US10620321B1 (en) 2008-08-29 2020-04-14 Interstate Electronics Corporation Systems and methods for tracking power modulation
US7986265B2 (en) * 2008-08-29 2011-07-26 Interstate Electronics Corporation Systems and methods for determining a rotational position of an object
US20100052981A1 (en) * 2008-08-29 2010-03-04 Alexander Steven B Systems and methods for determining a rotational position of an object
US8212195B2 (en) 2009-01-23 2012-07-03 Raytheon Company Projectile with inertial measurement unit failure detection
US8558153B2 (en) * 2009-01-23 2013-10-15 Raytheon Company Projectile with inertial sensors oriented for enhanced failure detection
US8269667B2 (en) 2009-05-15 2012-09-18 Mayflower Communications Company, Inc. GPS-based roll rate and roll angle measurement in the absence of jamming
US8106811B2 (en) * 2009-05-15 2012-01-31 Mayflower Communications Company, Inc. Antijam protected GPS-based measurement of roll rate and roll angle of spinning platforms
US20100289687A1 (en) * 2009-05-15 2010-11-18 Mayflower Communications Company, Inc. Antijam protected GPS-based measurement of roll rate and roll angle of spinning platforms
US8076622B1 (en) * 2009-08-31 2011-12-13 Rockwell Collins, Inc. Low profile, conformal global positioning system array for artillery
US8237096B1 (en) 2010-08-19 2012-08-07 Interstate Electronics Corporation, A Subsidiary Of L-3 Communications Corporation Mortar round glide kit
US9156372B1 (en) 2011-04-26 2015-10-13 Enovation Controls, Llc Multinodal ballast and trim control system and method
WO2013043097A1 (en) * 2011-09-20 2013-03-28 Bae Systems Bofors Ab Method and gnc system for determination of roll angle
EP2758741A4 (en) * 2011-09-20 2015-06-03 Bae Systems Bofors Ab Method and gnc system for determination of roll angle
US9354028B2 (en) 2011-09-20 2016-05-31 Bae Systems Bofors Ab Method and GNC system for determination of roll angle
US10608348B2 (en) 2012-03-31 2020-03-31 SeeScan, Inc. Dual antenna systems with variable polarization
US8718587B2 (en) * 2012-04-18 2014-05-06 Qualcomm Incorporated Reconfigurable LNA for increased jammer rejection
US20150263434A1 (en) 2013-03-15 2015-09-17 SeeScan, Inc. Dual antenna systems with variable polarization
US10490908B2 (en) 2013-03-15 2019-11-26 SeeScan, Inc. Dual antenna systems with variable polarization
US9115968B1 (en) * 2014-02-12 2015-08-25 The United States Of America As Represented By The Secretary Of The Army Course self-correcting projectile
US9366514B1 (en) * 2014-02-25 2016-06-14 Lockheed Martin Corporation System, method and computer program product for providing for a course vector change of a multiple propulsion rocket propelled grenade
US9645251B1 (en) * 2014-03-26 2017-05-09 Exelis Inc. Estimation of roll and roll rate of a spinning body based on a signal received from a remote transmitter
US10921464B1 (en) * 2015-05-29 2021-02-16 Interstate Electronics Corporation Satellite navigation receiver for a rapidly rotating object with improved resistance to jamming
US9983315B1 (en) * 2015-05-29 2018-05-29 Interstate Electronics Corporation Satellite navigation receiver for a rapidly rotating object with improved resistance to jamming
US10698119B1 (en) * 2015-05-29 2020-06-30 Interstate Electronics Corporation Satellite navigation receiver for a rapidly rotating object with improved resistance to jamming
US10705221B2 (en) * 2016-06-08 2020-07-07 The Boeing Company On-board backup and anti-spoofing GPS system
CN107152895B (en) * 2017-06-21 2018-08-17 北京瑞极通达科技有限公司 A kind of conformal radar survey height/global location set composite
CN107152895A (en) * 2017-06-21 2017-09-12 北京瑞极通达科技有限公司 A kind of conformal radar surveys height/global location set composite
CN107631666B (en) * 2017-09-29 2019-10-11 西安交通大学 A kind of body roll angle detection system and method based on earth magnetism and sun optic angle
CN107631666A (en) * 2017-09-29 2018-01-26 西安交通大学 A kind of body roll angle detecting system and method based on earth magnetism and sun optic angle
US11543539B2 (en) 2018-09-21 2023-01-03 Subaru Corporation Aircraft flight control apparatus, aircraft flight controlling method, and non-transitory storage medium
CN115659103A (en) * 2022-12-27 2023-01-31 北京航天众信科技有限公司 Method, device, medium and equipment for calculating roll angle of rotating target

Also Published As

Publication number Publication date
EP1606571A1 (en) 2005-12-21
AU2003290711A1 (en) 2004-11-23
WO2004097329A1 (en) 2004-11-11
CA2519935A1 (en) 2004-11-11
JP2006514258A (en) 2006-04-27

Similar Documents

Publication Publication Date Title
US6779752B1 (en) Projectile guidance with accelerometers and a GPS receiver
US6573486B1 (en) Projectile guidance with accelerometers and a GPS receiver
US6883747B2 (en) Projectile guidance with accelerometers and a GPS receiver
US7397422B2 (en) Method and system for attitude determination of a platform using global navigation satellite system and a steered antenna
US6266616B1 (en) Confused-in-space stellar attitude acquisition using multiple star trackers
CA2085847C (en) Autonomous precision weapon delivery using synthetic array radar
US4589610A (en) Guided missile subsystem
US7500636B2 (en) Processes and devices to guide and/or steer a projectile
US20030009284A1 (en) Lost-in-space stellar attitude acquisition using multiple star trackers
US7133776B2 (en) Attitude alignment of a slave inertial measurement system
Bezick et al. Inertial navigation for guided missile systems
US5253823A (en) Guidance processor
US5442560A (en) Integrated guidance system and method for providing guidance to a projectile on a trajectory
JP5338464B2 (en) Inertial navigation device, flying object, and navigation data calculation method
Klotz et al. GPS-aided navigation and unaided navigation on the joint direct attack munition
US9217639B1 (en) North-finding using inertial navigation system
US9207328B2 (en) System and method for determination of attitude for projectile
US6142412A (en) Highly accurate long range optically-aided inertially guided type missile
JPH04110600A (en) Lightweight missile guidance system
CN114578857A (en) Guidance aircraft autonomous control method, device and system based on full trajectory information
US11913757B2 (en) Constraining navigational drift in a munition
AU2018311656B2 (en) In-flight azimuth determination
CN117664129A (en) Marine launching self-alignment method and device suitable for solid rocket
Hepner et al. Pointer: Projectile orientation in navigation terms for a spinning body

Legal Events

Date Code Title Description
AS Assignment

Owner name: LITTON SYSTEMS, INC., CALIFORNIA

Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:RATKOVIC, JOSEPH A.;REEL/FRAME:014012/0531

Effective date: 20030319

FEPP Fee payment procedure

Free format text: PAYOR NUMBER ASSIGNED (ORIGINAL EVENT CODE: ASPN); ENTITY STATUS OF PATENT OWNER: LARGE ENTITY

FPAY Fee payment

Year of fee payment: 4

AS Assignment

Owner name: NORTHROP GRUMMAN SYSTEMS CORPORATION, CALIFORNIA

Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:NORTHROP GRUMMAN CORPORATION;REEL/FRAME:025597/0505

Effective date: 20110104

FPAY Fee payment

Year of fee payment: 8

REMI Maintenance fee reminder mailed
LAPS Lapse for failure to pay maintenance fees
STCH Information on status: patent discontinuation

Free format text: PATENT EXPIRED DUE TO NONPAYMENT OF MAINTENANCE FEES UNDER 37 CFR 1.362

FP Lapsed due to failure to pay maintenance fee

Effective date: 20160824